bluuebunny/crossref_metadata_2025 huggingface dataset:
Constructions, Lexical Semantics, and the Correspondence Principle: Accounting for Generalizations and Subregularities in the Realization of Arguments
Authors: GOLDBERG ADELE E.
Published: January 2010

Whether particular arguments are overtly realized in languages like English is not random. A number of researchers have put forward sweeping generalizations in order to capture certain general tendencies. This chapter, however, argues that these analyses underestimate the role of constructions, detailed lexical semantics and discourse factors. Given sufficient attention to these factors, the general tendencies, as well as productive classes of systematic exceptions, follow without additional grammatical stipulation.
4 Institutional Managerialism
Authors: CASS DEBORAH Z.
Published: January 2010

This chapter examines the constitutionalization form of institutional managerialism. It argues that under institutional managerialism, constitutionalization occurs by way of management of policy diversity between states by institutions and rules, which are given the imprimatur of a ‘constitutional’ character. It presents itself as a natural deduction from factual developments, which are presented as existing beyond the law, and yet proponents of this approach also aspire to change the WTO system and other facts of the wider economic order.
5 Rights-Based Constitutionalization
Authors: CASS DEBORAH Z.
Published: January 2010

This chapter discusses rights-based constitutionalization. This model is aspirational in character — an argument for what the system should be, and not what it is. According to this view, constitutionalization should be promoted, and it should be a constitutionalization process in which a right to trade is recognized. It is argued that rights-based constitutionalization is inconsistent with traditional methods for the incorporation and transformation of rules into international law. The theory behind the model is based on an unnecessary and outdated opposition between State and individual, and it is an over-ambitions and evangelical model which attempts to ‘hijack’ traditional human rights’ legitimacy.
7 Anti-Constitutionalization
Authors: CASS DEBORAH Z.
Published: January 2010

This chapter argues that not only is constitutionalization descriptively inappropriate, it is also normatively undesirable. This position, termed the anti-constitutionalization critique, contends that constitutionalization contracts the capacity of states to decide matters of national interest; is weakly deliberative in form; emphasizes economic goals at the expense of other values; ignores the important contributions of private law to any constitution rules for international economic order; and is self-legitimating.
The Principles of the Law of Restitution
Authors: Virgo Graham
Published: January 2010

This book lays out the key principles underlying the law of restitution, a subject recognised by the House of Lords as a discrete body of law fifteen years ago. The law of restitution is concerned with the questions of when restitutionary remedies may be awarded. These are remedies which operate to deprive defendants of gains rather than to compensate claimants for losses. The traditional approach to the subject assumes that restitutionary remedies are only available to reverse unjust enrichment. This book asserts that restitutionary remedies are triggered by three different types of action: the reversal of the defendant's unjust enrichment, the commission of a wrong by the defendant, and the vindication of the claimant's property rights. Since the publication of the first edition of this book this model has increasingly been recognised by the courts. In this book, the law is examined through analyses of key cases and relevant statutory provisions, demonstrating the way in which the law in used to solve a wide variety of legal problems in a number of jurisdictions. The very different views of academics on the nature and ambit of the subject are also carefully considered. The result will be invaluable to students on restitution courses at every level, practitioners and those engaged in research on the subject.
The Principle of Unjust Enrichment
Authors: Virgo Graham
Published: January 2010

Although the unjust enrichment principle often operates positively, in the sense that the claimant must establish that the defendant has been unjustly enriched before restitution is available, sometimes the principle may operate negatively. This is because restitutionary relief may be awarded to prevent the defendant from becoming unjustly enriched. Even though the unjust enrichment principle has been clearly recognised at the highest level, the place of that principle within the law of obligations and the function of the principle still require careful justification. A number of commentators have suggested that restitutionary liability should be based on some other theoretical foundation, including proprietary theory, no unifying principle of unjust enrichment, and unconscientious retention. Possible functions of the unjust enrichment principle are discussed, namely, the formulaic function and the normative function. The approach adopted by England with respect to the function of the unjust enrichment principle is also considered.
Principles Underlying the Recognition of the Grounds of Restitution
Authors: Virgo Graham
Published: January 2010

Since a restitutionary claim founded on the reversal of the defendant's unjust enrichment will only succeed if the claimant establishes that the claim falls within one of the recognised grounds of restitution, or within a ground of restitution which can be deduced from one of the recognised grounds of restitution, it is vital to be aware of what the grounds of restitution are and also why they have been recognised. Every ground of restitution can be explained by reference to at least one of three different principles — claimant-oriented, defendant-oriented, and policy-oriented — but quite often more than one of them may be operating. This chapter discusses claimant-oriented grounds of restitution (absence of intention, vitiated intention, and qualified intention), defendant-oriented grounds of restitution (exploitation and free acceptance), and policy-oriented grounds of restitution. Four additional considerations in grounds of restitution are: the danger of over-simplification, the grounds of restitution are not closed, the relevance of the type of enrichment, and restitution and third parties.
Ignorance
Authors: Virgo Graham
Published: January 2010

Although ignorance has never been recognised by the courts as a ground of restitution in its own right, it has been invoked to explain why restitution has been ordered in a number of cases. In many cases it will in fact make no difference whether the claimant's restitutionary claim is founded on unjust enrichment, with ignorance constituting the ground of restitution, or on the vindication of property rights, with the claimant's ignorance being used to explain why title did not pass to the defendant. Where, however, the claimant's property is transferred indirectly to the defendant without the claimant's knowledge, the unjust enrichment action cannot assist the claimant, primarily because of the insurmountable obstacle of showing that the enrichment received by the defendant was received at the expense of the claimant. This chapter discusses the role of ignorance as a ground of restitution, services provided in circumstances of ignorance, interceptive subtraction, and election between principles.
Exploitation
Authors: Virgo Graham
Published: January 2010

Like compulsion, exploitation is not a ground of restitution in its own right but is a general principle on which a number of specific grounds of restitution are founded. Exploitation enables a number of disparate grounds of restitution to be treated together. These grounds have the common characteristic that the defendant has actually taken advantage of the claimant's weaker position in some way, or can at least be presumed to have taken advantage of the claimant. The essence of exploitation consequently involves the actual or potential abuse of power by the defendant. The grounds of restitution which are founded on the principle of exploitation can be considered to be both claimant- and defendant-oriented. This chapter discusses the relationship between exploitation and other principles, identification of enrichment, vitiation of transactions for exploitation, relationship between exploitation and wrongdoing, the essence of undue influence as a ground of restitution, abuse of fiduciary relationships of confidence, and unconscionable conduct.
Necessity
Authors: Virgo Graham
Published: January 2010

In the same way that there are general principles of compulsion and exploitation on which a number of specific grounds of restitution are based, there is also a general principle of necessity by reference to which a number of specific grounds of restitution can be identified. Although the existence of a general principle of necessity is beyond doubt in English law, the principle is not well developed in common law legal systems. The predominant reason for the underdeveloped nature of the necessity principle is because of the importance of the principle of officiousness which operates to bar restitutionary claims. The success of restitutionary claims grounded on necessity will depend on how the principle of officiousness is defined. This chapter discusses the principle of necessity, the principle of officiousness, identification and valuation of enrichment, necessitous intervention by a stranger, agency and other pre-existing legal relationships, and necessity in the context of maritime adventures.
Restitution for Breach of Contract
Authors: Virgo Graham
Published: January 2010

Where the defendant has breached a contract, the claimant can obtain damages which are assessed by reference to any loss or injury which he or she has suffered. In general, the purpose of such damages is to place the claimant in the position he or she would have been in had the contract not been breached. This involves the protection of the so-called ‘expectation interest’ and ‘reliance interest’. This chapter examines whether there is a third interest which should be protected by the award of damages where the defendant has breached a contract, namely, the ‘restitution interest’. The general principle denying restitution for breach of contract is discussed, along with methods for awarding restitutionary remedies for breach of contract (identification of a fiduciary relationship, tortious wrongdoing, and price payable for interference with property rights).
Restitution for Equitable Wrongdoing
Authors: Virgo Graham
Published: January 2010

Where the defendant has breached an equitable duty which he or she owed to the claimant, a restitutionary relief is available. The defendant can be deterred from exploiting the relationship by ensuring that, at the very least, the value of any benefit which he or she obtained from the breach of duty should be paid to the claimant to whom the duty was owed. Where the defendant is more culpable in breaching his or her equitable duty, a more extensive form of restitutionary remedy may be available. This chapter examines the rationale behind the award of restitutionary remedies for equitable wrongdoing, types of remedy which are available for equitable wrongdoing (account of profits, proprietary remedies, interest, and equitable compensation), and categories of equitable wrongdoing including breach of fiduciary duty, breach of confidence, unconscionability, and dishonestly inducing or assisting in a breach of trust or fiduciary duty.
Criminal Offences
Authors: Virgo Graham
Published: January 2010

When an offender has committed a criminal offence, the law of restitution may be relevant in two ways. First, the offender may have received a benefit as a result of the commission of the crime, so the question for the law of restitution is whether there is a cause of action which will enable the victim or the State to recover the proceeds of the crime. Secondly, a consequence of the offender committing the crime may be that he or she is entitled to obtain a benefit, and the question is whether the offender can be prevented from obtaining this benefit. This chapter discusses the general principles and policies underlying criminal offences, and restitutionary claims brought by the victim (claims founded on unjust enrichment, claims founded on the vindication of property rights, claims founded on wrongdoing, torts and breaches of fiduciary duty, and restitution from third parties). Restitutionary claims brought by the State are discussed, along with denial of benefits arising from the commission of crimes, the forfeiture principle and its rationale, and the forfeiture rule.
Defences Arising from Changes in the Defendant's Circumstances
Authors: Virgo Graham
Published: January 2010

Sometimes the defendant's circumstances will change to such an extent after he or she has obtained a benefit that it is no longer just for the defendant to make full restitution of the benefit received. In such cases, the defendant may be able to rely on one of three defences to defeat or circumscribe the claimant's restitutionary claim, namely, estoppel, payment by an agent to his or her principal, and change of position. The availability of each defence will depend on the reason why the defendant's circumstances have changed. This chapter discusses the conditions for establishing the defence of estoppel, including reliance by the defendant, change of circumstances, and the justice of the case; consequence of the claimant being estopped; transfer of a benefit by an agent to his or her principal; and relationship between change of position and other defences such as estoppel, the agent's defence, and bona fide purchase.
Passing On and Mitigation of Loss
Authors: Virgo Graham
Published: January 2010

Whereas the defences of estoppel, transfer by an agent to his or her principal, and change of position are assessed by reference to changes in the circumstances of the defendant, usually after he or she has received a benefit, this chapter examines whether there are, and if not whether there should be, any defences in English law which operate by reference to changes in the circumstances of the claimant after the receipt of the benefit by the defendant. There are two possible defences which, if they are recognised, would operate in this way: passing on and mitigation of loss. The general principle of passing on is discussed, along with judicial examination of the defence (recognition or rejection of the defence), and whether the defence of passing on should be recognised.
The Personal Employment Contract
Authors: Freedland Mark
Published: January 2010

This book is an analytical study of the current English law of traditional contracts of employment and of other personal employment contracts. Concentrating on the common law basis of individual employment law, it takes full account of relevant British and European Community legislation up to and including the Employment Act 2002, and considers the impact of the Human Rights Act 1998 and of the developing law of human and social rights more generally. This book takes account of the very considerable amount of case-law, legislation, and legal writing which has affected the law of the contract of recent employment. This book addresses a wide range of employment relationships; in fact, it argues for and is constructed around a whole new category of employment contracts, which includes not only contracts of employment but also other ‘personal employment contracts’, a concept which the book articulates and justifies. Within that novel conceptual framework, many of the major features of the law of employment contracts are re-examined and presented in unfamiliar and challenging terms. Thus, the employer is re-conceptualized as the ‘employing enterprise’, the bilateral structure of employment contracts is re-evaluated, and new explanations are advanced for the functioning of the law of termination of employment contracts and of remedies for wrongful termination.
Definition and Personal Structure
Authors: FREEDLAND FBA MARK R.
Published: January 2010

This chapter begins with an analysis of how employment law came to be organized around the category of the contract of employment, to which a false unity was attributed. It explains how the contract of employment came to be systematically contrasted with another contract type, that of the contract for services, arguing that this distinction has proved to be an equally false or unsatisfactory one. As a result, it has become difficult to decide whether certain employment relationships, or sets of arrangement for employment, fall into any of those contractual categories and if so which of them. The second section of the chapter suggests a set of definitions and distinctions which might provide greater clarity and coherence in the foundational aspect of the law of employment contracts. The third section demonstrates the gains in clarity of analysis which can be obtained by operating within the expanded category of personal employment contracts rather than within the traditional and narrower category which has dominated employment law.
Towards a Codification of Personal Work Contracts—Relation and Contract in Employment Law
Authors: FREEDLAND FBA MARK R.
Published: January 2010

This chapter argues that the expansion and restatement of the law of the contract of employment is a feasible and useful project. However, the complete execution of it would consist of an authoritative codification of the law of personal work or employment contracts. If that larger project would be undertaken in the future, this would involve a heavy investment of creative energy on the part of those concerned with the theoretical and practical development of employment law. The chapter considers whether the preliminary work has indicated that this would be a sound investment both in practical and theoretical terms.
The Decline of the Ottoman Empire in the Middle East and the ‘Arab Awakening’ before 1914
Authors: Fieldhouse D. K.
Published: January 2010

One historic development that took place before the Arab Middle East became what it was after 1914 was the decline of the power of the Ottoman empire that had ruled the region from varying dates in the 16th century. This chapter examines how far the dissolution of the Ottoman empire could be attributed to a new and explosive awakening of Arab nationalism, a desire to cast off Turkish rule and form new nation states. In particular, this chapter explores whether there was an ‘Arab Awakening’ (a phrase associated with George Antonius) before 1914 and between then and 1918, how strong it was, and whether it could, by itself, have brought about the dissolution of the Ottoman Arab empire.
Britain in Mesopotamia/Iraq, 1918–1958
Authors: Fieldhouse D. K.
Published: January 2010

This chapter examines British rule in Mesopotamia/Iraq during the years 1918-1958. There were two dominant features of the British position in Mesopotamia (now known as Iraq) that were largely to influence its history until, and in fact after, the end of the mandate in 1932. First, as in the other mandates, Britain’s position there was ambiguous as the very concept of a mandate was new and undefined. The second fundamental feature of post-1918 Iraq was that it had no historical, religious, or ethnic homogeneity. In this chapter, the British experience in Iraq will be examined under four heads: first, the indigenous social structure; second, the early British response to 1932; third, Iraqi politics and society from 1920 to 1941; and finally, the revival, decline, and fall of British influence, 1941 to 1958.
Palestine: The British Mandate, 1918–1948
Authors: Fieldhouse D. K.
Published: January 2010

This chapter examines the British mandate in Palestine from 1918 to 1948 and why Palestine was arguably the greatest failure in the whole history of British imperial rule. The British, after thirty years of colonial rule, had failed to create a viable indigenous government of any sort in Palestine and could only evacuate the country and leave its future to be decided by civil war. The reasons for this failure are discussed based on the position and reactions of each of the three main actors: the Arabs, the Zionists, and the British. Any one of these might have blocked the road to an agreed inter-communal settlement.
Lebanon and the French, 1918–1946
Authors: Fieldhouse D. K.
Published: January 2010

This chapter investigates the French mandate in Lebanon from 1918 to 1946. The modern history of Lebanon began in 1920, when the French, the prospective mandatory, created a state which they called Le Grand Lebanon (Greater Lebanon). Since this state had no historic unity its later development depended on whether this amalgam of Ottoman districts and religious sects could hold together and generate a sense of common nationhood. Because this was necessarily largely a political process, this chapter examines political structures and developments by focusing on the establishment of the French mandate and its background and the operation of the mandate to 1945.
Conclusions
Authors: Fieldhouse D. K.
Published: January 2010

The central question addressed by this book is the effect the mandates held by Britain and France had on the one-time provinces of the Ottoman empire in the Middle and Near East. Although the mandates, or some comparable form of western rule, became inevitable once Ottoman rule had been destroyed, they did not fulfil the expectations of those idealists who drew up the guidelines for the system. Britain and France were there for strategic, economic, and ideological purposes, and it was no part of their ambitions to undertake a fundamental social and political reconstruction that might, in the longer term, have generated truly democratic and stable societies. They left when it was no longer convenient to stay, leaving behind a multitude of unresolved tensions and potential conflicts that would eventually grow into the complex of tensions and despotisms characteristic of modern-day Middle East.
The Universe in a Helium Droplet
Authors: Volovik Grigory E.
Published: January 2010

There are fundamental relations between three vast areas of physics: particle physics, cosmology, and condensed matter physics. The fundamental links between the first two areas — in other words, between micro- and macro-worlds — have been well established. There is a unified system of laws governing the scales from subatomic particles to the cosmos and this principle is widely exploited in the description of the physics of the early universe. This book aims to establish and define the connection of these two fields with condensed matter physics. According to the modern view, elementary particles (electrons, neutrinos, quarks, etc.) are excitations of a more fundamental medium called the quantum vacuum. This is the new ‘aether’ of the 21st century. Electromagnetism, gravity, and the fields transferring weak and strong interactions all represent different types of the collective motion of the quantum vacuum. Among the existing condensed matter systems, a quantum liquid called superfluid 3He-A most closely represents the quantum vacuum. Its quasiparticles are very similar to the elementary particles, while the collective modes are analogues of photons and gravitons. The fundamental laws of physics, such as the laws of relativity (Lorentz invariance) and gauge invariance, arise when the temperature of the quantum liquid decreases.
Gravity
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter discusses the Einstein theory of gravity, which consists of two main elements: (1) gravity is related to a curvature of space-time in which particles move along geodesic curves; and (2) dynamics of the metric field is determined by Einstein equations. Sakharov theory of gravity, in which gravity is induced by vacuum fluctuations, reproduces Einstein theory. The effective gravity emerging in quantum liquids is similar to Sakharov gravity, but in quantum liquids only the first element of Einstein theory is present — the effective metric for quasiparticles, while the metric field obeys hydrodynamic type equations instead of Einstein equations. The chapter also introduces the cosmological constant problem. In particle physics, field quantization allows a zero-point energy, the constant vacuum energy when all fields are in their ground states. In the absence of gravity the constant energy can be ignored, since only the difference between the energies of the field in the excited and ground states is meaningful. In the Einstein theory of gravity, however, the gravitational field reacts to the total value of the energy momentum tensor of the matter fields, and thus the absolute value of the vacuum energy becomes meaningful. If the energy momentum tensor of the vacuum is non-zero it must be added to the Einstein equations. The corresponding contribution to the action is given by the cosmological term, which was introduced by Einstein.
Effective Theory Of Superfluidity
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter discusses how the effective theory incorporates the low-energy dynamics of the superfluid vacuum and the dynamics of the system of quasiparticles in Bose liquids. The effective theory of two-fluid hydrodynamics was developed by Lev Landau. According to the general ideas of Landau, a weakly excited state of the quantum system can be considered as a small number of elementary excitations. Applying this to the quantum liquid 4He, the dense system of strongly interacting 4Heatoms can be represented in the low-energy corner by a dilute system of weakly interacting quasiparticles (phonons and rotons). In addition, the state without excitations — the ground state or the quantum vacuum — has its own degrees of freedom: it can experience the coherent collective motion. This motion is described by continuity and London equations for superfluid velocity and density. Since superfluid velocity and density of liquid produce effective acoustic metric for quasiparticles, the continuity and London equations represent an analog of Einstein equations for effective gravity in quantum liquids, while quasiparticles represent matter on the background of quantum vacuum. The chapter also considers the role of Galilean transformation, two reference frames for quasiparticles (co-moving and absolute), effect of frame dragging produced by superfluid velocity, and whether the speed of light is a fundamental constant.
Advantages and Drawbacks Of Effective Theory
Authors: GRIGORY E. VOLOVIK
Published: January 2010

The energy momentum tensor for the vacuum field which represents gravity is non-covariant, since the effective gravitational field obeys hydrodynamic equations rather than Einstein equations. However, even for the fully covariant dynamics of gravity, in Einstein theory the corresponding quantity ‘the energy momentum tensor for the gravitational field’ cannot be presented in the covariant form. This is the famous problem of the energy momentum tensor in general relativity. One must sacrifice either covariance of the theory or the true conservation law. From the condensed matter point of view, the inconsistency between the covariance and the conservation law for the energy and momentum is an aspect of the much larger problem of the non-locality of effective theories. This chapter discusses the advantages and drawbacks of effective theory, non-locality in effective theory, true conservation and covariant conservation, covariance versus conservation, paradoxes of effective theory, Novikov–Wess–Zumino action for ferromagnets as an example of non-locality, effective versus microscopic theory, whether quantum gravity exists, what effective theory can and cannot do, and universality classes of effective theories of superfluidity.
Microscopic Physics
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter deals with the Fermi systems, where the low-energy effective theory involves both bosonic and fermionic fields. Above the phase transition to the superconducting or superfluid state, the overwhelming majority of systems consisting of fermionic particles (electrons in metals, neutrons in neutron stars, 3He atoms in 3He liquid, etc.) form a so-called Fermi liquid. Below transition new types of fermionic vacua emerge. This chapter discusses the Bardeen–Cooper–Schrieffer (BCS) theory for spin-triplet superfluids, which provide examples of different universality classes of fermionic vacua: fully gapped vacua, vacua with stable and marginal point nodes — Fermi points, and vacua with nodal lines — Fermi lines. It also discusses emergent ‘relativistic’ quasiparticles, fundamental constants and hierarchy of Planck energy scales in fermionic systems, problem of vacuum energy and cosmological term in bi-metric gravity, and mass generation for Standard Model fermions.
Universality Classes Of Fermionic Vacua
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter discusses effective theories of quantum fermionic liquids. In the low-energy limit, the type of the effective theory depends on the structure of the quasiparticle spectrum, which in turn is determined by topology in momentum space (p-space topology). The p-space topology distinguishes three main generic classes of the stable fermionic spectrum in the quantum vacuum of a 3+1 fermionic system: vacua with Fermi surfaces, vacua with Fermi points, and vacua with a fully gapped fermionic spectrum. Fermi surface is stable because it represents the topological object — the vortex in momentum space. As a result, Fermi liquids with Fermi surface share the properties of their simplest representative: weakly interacting Fermi gas. The low-energy physics of the interacting particles in a Fermi liquid is equivalent to the physics of a gas of quasiparticles moving in collective Bose fields produced by all other particles. Another topological object in p-space is the hedgehog, which is responsible for stability of Fermi points. Example of vacuum of the Fermi-point universality class is provided by 3He-A. Near the Fermi point the effective relativistic field theory emerges with emerging Weyl fermions, gauge fields, and gravity. The chapter discusses p-space and r-space topology, topological invariant for Fermi surface and Fermi points in terms of Green's function, Landau and non-Landau Fermi liquids, collective modes of the Fermi surface, volume of the Fermi surface as invariant of adiabatic deformations, collective modes of vacuum with Fermi points (electromagnetic and gravitational fields), and manifolds of zeros in p-space of higher dimensions.
Vortices In 3He-B
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter discusses the topology of singular topological defects — defects with singular core of coherence length size — in 3He-B and in quantum chromodynamics, such as conventional mass vortices, spin vortices, axion and pion strings, hedgehogs, monopoles, and vortons. The Casimir force between spin and mass vortices in 3He-B leads to formation of a composite defect — spin-mass vortex, which is stabilized in rotating cryostat. Spin-mass vortex serves as string terminating topological soliton. Topological confinement of two spin-mass vortices by soliton leads to another composite object observed in 3He-B — doubly quantized vortex. The chapter also discusses the symmetry of defects, the interplay of symmetry and topology, the symmetry of hedgehogs and monopoles, spherically symmetric objects in superfluids, enhanced superfluidity in the core of hedgehog, spontaneously broken parity, and axial symmetry in the core of 3He-B vortices. Vortex with spontaneously broken parity in the core represents analog of Witten superconducting cosmic string. The observed twist of the core corresponds to supercurrent along the Witten string.
Monopoles and Boojums
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter is devoted to point defects such as hedgehogs, Dirac magnetic monopoles, 't Hooft–Polyakov monopole, and nexus. Some of these objects represent composite defects resulting from a hierarchy of energy scales with different symmetries. Examples are the hedgehog-monopole, which serves as a termination point of vortex-string, and nexus which represents the magnetic pole with emanating flux. In chiral superconductors the magnetic flux to the nexus can be supplied by four half-quantum vortices. Due to topological confinement chiral superconductor represents the natural trap for 't Hooft–Polyakov monopole. The chapter also discusses topology of boojums — point and line defects living at surfaces of the ordered system or at the interface between different vacua. Examples are provided by defects at the interface between 3He-A and 3He-B, including Alice string. In many cases these defects represent composite objects. For example, boojum on the A-phase side of the interface is the termination point of the vortex living on the B-phase side. Vortex sheet is discussed which is formed at the interface between 3He-A and 3He-B in rotating cryostat. It separates the vortex lattice in 3He-A, which experiences the solid body rotation, and the vortex free 3He-B.
Anomalous Non-Conservation Of Fermionic Charge
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter opens the discussion of physical phenomena in the vacuum with Fermi points. The non-trivial topology in the momentum space leads to anomalies produced by the massless chiral fermions in the presence of collective fields such as magnetic field, textures, and vortices. In 3He-A, this gives rise to the anomalous mass current, the paradox of the orbital angular momentum, etc. All these phenomena are of the same origin as the chiral anomaly in relativistic quantum field theories. For example, the momentum exchange between superfluid vacuum and quasiparticles in 3He-A is analogous to electroweak baryoproduction — formation of excess of matter over anti-matter due to chiral anomaly. This allowed for the measurement of the spectral-flow force acting on a vortex-skyrmion in superfluid in 3He-A to experimentally verify the Adler–Bell–Jackiw equation describing chiral anomaly in particle physics. The chapter also discusses the Novikov–Wess–Zumino action, the interplay between r-space and p-space topology relevant for the discussed phenomena, and introduces 3 reactive forces acting on a vortex in fermionic superfluids: Magnus, Iordanskii, and Kopnin forces.
Anomalous Currents
Authors: GRIGORY E. VOLOVIK
Published: January 2010

Parity violation, the asymmetry between left and right, is one of the fundamental properties of the quantum vacuum of the Standard Model. This effect is strong at high energy on the order of the electroweak scale, but is almost imperceptible in low-energy condensed matter physics. At this scale the left and right particles are hybridised and only the left-right symmetric charges survive. An analog of parity violation exists in superfluid 3He-A alongside related phenomena such as chiral anomaly and macroscopic chiral currents. The fermionic charge of right-handed particles minus that of left-handed ones is conserved at the classical level but not if quantum properties of the physical vacuum are taken into account. This charge can be transferred to the inhomogeneity of the vacuum via the axial anomaly in the process of helical instability. The inhomogeneity which absorbs the fermionic charge arises as a hypermagnetic field configuration in the Standard Model and as vortex texture in 3He-A. This allowed the experimental simulation of magnetogenesis (generation of hypermagnetic field) in 3He-A. Chern–Simons energy term in the Standard Model and in 3He-A is also discussed, where the effective chemical potential for chiral fermions is provided by counterflow velocity: relative velocity of motion of normal component of the liquid with respect to the superfluid one.
Macroscopic Parity-Violating Effects
Authors: GRIGORY E. VOLOVIK
Published: January 2010

The chiral anomaly phenomenon in relativistic quantum field theory can also be mapped to the angular momentum paradox in 3He-A, which has possibly a common origin with the anomaly in the spin structure of hadrons. To relate the chiral anomaly and angular momentum paradox in 3He-A, it is necessary to consider the parity effects which occur for the system of chiral fermions under rotation. This chapter discusses macroscopic parity violation, mixed axial gravitational Chern–Simons term, parity-violating current, parity-violating action in terms of gravimagnetic field, orbital angular momentum in 3He-A, and the odd current in 3He-A — sensitivity of the normal component density to the direction of rotation, which is the counterpart of the parity-violating effects in relativistic theories with chiral fermions. There is no real parity violation in 3He-A. However, a non-zero expectation value of the axial vector of the orbital angular momentum indicates a spontaneously broken reflectional symmetry, and an inner observer living in 3He-A would consider this effect as true parity violating.
Quantization Of Physical Parameters
Authors: GRIGORY E. VOLOVIK
Published: January 2010

The dimensional reduction of the 3+1 system with Fermi points brings the anomaly to the (2+1)-dimensional systems with fully gapped fermionic spectrum. The most pronounced phenomena in these systems are related to spin and quantum statistics of the topological objects in 2+1 systems — skyrmions and to the quantisation of physical parameters, such as Hall and spin-Hall conductivity and fermionic charge. This quantization is determined by the integer valued momentum-space topological invariant expressed via the Green's function, which is discussed in Chapter 11, and demonstrates the interplay of p-space and r-space topologies. The Chern–Simons term is the r-space invariant (such as the Hopf invariant), while its prefactor is expressed in terms of p-space invariant. In general case the mixed Chern–Simons term composed of different effective gauge fields has the prefactor in terms p-space invariant supported by symmetry. Such Chern–Simons terms give rise to different types of intrinsic Hall and spin-Hall effect. The fully gapped vacua with different values of physical parameters are separated by topological quantum phase transition with gapless intermediate states.
Edge States and Fermion Zero Modes on Soliton
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter opens the part of the book devoted to fermions living in the core of topological objects. If fermions in bulk are fully gapped, then at low temperature they are frozen out, and only gapless fermions living in the low dimensional world of the core of topological object survive. This reproduces the popular idea that we live on a membrane (brane) embedded in higher-dimensional space. In this view, our 3+1 space-time spans the extended coordinates of the brane, while the other (extra) dimensions are of the order of the core size. This chapter discusses fermion zero modes — gapless fermions, which live inside solitons and domain walls separating vacua with different values of topological invariants in 2+1 and 4+1 dimensions. The index theorem is demonstrated which expresses the number of fermion zero modes at the interface via the difference of topological invariants of gapped vacua on two sides of the interface. The index theorem is derived using topology in combined (p,r) space and dimensional reduction. The fermion zero modes living at the interface embedded in 4+1 space represent chiral 3+1 fermions, which belong to universality class of Fermi point.
Spectral Flow in The Vortex Core
Authors: GRIGORY E. VOLOVIK
Published: January 2010

There are four forces acting on a vortex moving with respect to normal and superfluid components of the liquid: three reactive forces (Magnus, Iordanskii, and Kopnin forces) and the Stokes friction force. The Iordanskii force comes from the analog of the gravitational Aharonov–Bohm effect and are discussed later in the book. The Kopnin or spectral flow force appears only in fermionic superfluids. This chapter discusses the Kopnin force acting on a singular vortex. The origin of this force is the phenomenon of chiral anomaly, but as distinct from the force acting on continuous vortex discussed in Chapter 18, the Adler–Bell–Jackiw equation for chiral anomaly is not applicable. The anomaly is now related to the spectral flow of fermion zero modes in the vortex core, which is caused by motion of the vortex with respect to the normal component. The spectral flow leads to generation of linear momentum by a vortex core, which is then transferred to the normal component. This process is similar to the generation of baryonic charge by the cores of cosmic strings and serves as the analog of Callan–Harvey mechanism of cancellation of anomalies. The temperature dependence of the spectral flow force is obtained from solution of kinetic equation for fermion zero modes. The resulting force acting on a vortex has been measured in experiments on vortex dynamics in 3He-B. Existence of two forces in addition to conventional Magnus and friction forces — Iordanskii and Kopnin forces – has been verified.
Landau Critical Velocity
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter opens the part of the book devoted to the nucleation of excitation of the vacuum — quasiparticles and topological defects. The superfluid vacuum flows with respect to environment (the container walls) without friction until the relative velocity becomes so large that the Doppler-shifted energy of excitations becomes negative in the frame of the environment, and these excitations can be created from the vacuum. The threshold velocity at which excitations of a given type acquire for the first time the negative energy is called the Landau critical velocity. In terms of the effective metric in superfluids, the region where the quasiparticle energy is negative represents the ergoregion, and in some geometry of flow — the event horizon. Nucleation of quasiparticles is also similar to electron-positron pair production in strong electric fields. The chapter also discusses thermal nucleation of vortices, which corresponds to sphaleron in high-energy physics, vortex nucleation by hydrodynamic instability and by macroscopic quantum tunnelling (the vortex instanton). The macroscopic action for vortices is used, which is topological and leads to quantization of particle number in quantum vacuum.
Vortex Formation By Kelvin–Helmholtz Instability
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter discusses nucleation of vortices due to instability of the interface between two superfluids moving with different velocities. The classical counterpart of this instability is the Kelvin–Helmholtz instability. In quantum liquids, there are two thresholds. The motion of superfluids with respect to the normal component becomes unstable when the Landau critical velocity for the surface excitations — ripplons — is reached and the ripplon energy becomes negative. In the shallow water limit, when ripplons acquire relativistic spectrum and obey the effective metric discussed in Chapter 32, the region with negative energy becomes analog of ergoregion or event horizon, and nucleation of ripplons at the Landau threshold becomes equivalent to Hawking radiation. However, if this process is sufficiently slow the second threshold can be reached, which is equivalent to Kelvin–Helmholtz criterion and corresponds to singularity in the centre of the black hole in the effective gravity for ripplons. In experiments with the interface between 3He-A and 3He-B, the onset of the Landau instability is marked by the appearance of the vortex lines in 3He-B, which are monitored in NMR measurements. Vortices appear at the non-linear stage of the growth of instability.
Vortex Formation in Ionizing Radiation
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter discusses the vortex formation during a rapid phase transition from the normal to superfluid state. The formation of topological defects in non-equilibrium phase transitions is a very generic phenomenon, called the phase ordering, which reflects the process of the establishment of the homogeneous order parameter state after quench. In cosmology this process is known as the Kibble–Zurek mechanism of formation of a network of cosmic strings when the cosmological phase transition is crossed in the expanding universe. In superfluid 3He-B, vortices are formed by neutron radiation. The decay products from the neutron absorption reaction generate ionization tracks, which cause heating in a small volume of 3He above the superfluid transition. Subsequently the heated bubble cools back below the transition temperature into the broken-symmetry state, and vortices are formed according to the Kibble–Zurek scenario. This chapter also discusses formation of vortices behind the propagating front of the second-order transition and due to instability of the non-topological vortex sheet.
Topological Defects As Source Of Non-Trivial Metric
Authors: GRIGORY E. VOLOVIK
Published: January 2010

Topological defects in 3He-A represent the topologically stable configurations of the order parameter. Since some components of the order parameter serve as the metric field of effective gravity, one can use the defects as the source of the non-trivial metric. This chapter considers two such defects in 3He-A, the domain wall, and disclination line. In general relativity, these defects correspond respectively to planar and linear singularities in the field of vierbein, at which the metric is degenerate. The static domain wall is analogous to the surface of infinite red shift in general relativity. The quantum mechanical communication between the worlds on two sides of the wall is considered. Disclination gives rise to the effective conical space for quasiparticles, with curvature concentrated on the disclination. The effective space outside the disclination core is flat, but the proper length of the circumference of radius R around the axis depends on the type of disclination and can be smaller or larger than 2πR. In the latter case the disclination is analogous to the anti-gravitating cosmic string.
Vacuum Under Rotation and Spinning Strings
Authors: GRIGORY E. VOLOVIK
Published: January 2010

This chapter deals with the properties of the quantum vacuum in superfluids in the presence of the analog of a gravimagnetic field. Such an effective field arises either in the presence of conventional U(1)-vortices, or under rotation which is equivalent to the constant in the space gravimagnetic field. A quantized vortex in 3He-A is another example of linear topological defects in the vierbein field at which the metric is degenerate. Vortices in superfluid 4He serve as analog of the spinning cosmic string, whose rotational angular momentum is concentrated in the string core. Effective gravimagnetic field concentrated in the core of the vortex produces the Aharonov–Bohm tube with gravimagnetic flux. It gives rise to the Iordanskii force acting on a vortex and to effective frame dragging for quasiparticles. The phenomenon of frame dragging by a rotating body is known as the Lense–Thirring effect. Rotation of or in the vacuum gives rise to Sagnac effect and to quantum friction experienced by a body rotating in the superfluid vacuum. The latter is analog of the Zel'dovich–Starobinsky effect, in which any body rotating in quantum vacuum, including the rotating black hole, radiates and looses its angular momentum. Emission of phonons and rotons from a body rotating in superfluid 4He occurs by quantum tunnelling of these quasiparticles from a body into the ergoregion.