bluuebunny/crossref_metadata_2025_split huggingface dataset:
Euclidean path integrals and quantum mechanics (QM)
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
Functional integrals are basic tools to study first quantum mechanics (QM), and quantum field theory (QFT). The path integral formulation of QM is well suited to the study of systems with an arbitrary number of degrees of freedom. It makes a smooth transition between nonrelativistic QM and QFT possible. The Euclidean functional integral also emphasizes the deep connection between QFT and the statistical physics of systems with short-range interactions near a continuous phase transition. The path integral representation of the matrix elements of the quantum statistical operator e-β H for Hamiltonians of the simple separable form p2/2m +V(q) is derived. To the path integral corresponds a functional measure and expectation values called correlation functions, which are generalized moments, and related to quantum observables, after an analytic continuation in time. The path integral corresponding to the Euclidean action of a harmonic oscillator, to which is added a time-dependent external force, is calculated explicitly. The result is used to generate Gaussian correlation functions and also to reduce the evaluation of path integrals to perturbation theory. The path integral also provides a convenient tool to derive semi-classical approximations.
Critical phenomena: Corrections to scaling behaviour
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
In preceding chapters, while deriving the scaling behaviour of correlation functions, we have always kept only the leading term in the critical region. We examine now the different corrections to the leading behaviour. For instance, when we have solved the renormalizaton group (RG) equations, so far, we have neglected the small deviation of the effective coupling constant from its fixed-point value. Moreover, to establish RG equations, we have neglected corrections subleading by powers of the cut-off, and effects of other couplings of higher canonical dimensions. Subleading terms related to the value of the effective coupling constant which give the leading corrections, at least near four dimensions, can easily be derived from the solutions of the renormalization group (RG) equations and are discussed first. The situations below and at four dimensions (the upper-critical dimension) have to be examined separately. The second type of corrections involves additional considerations and is examined in the second part of the chapter. The last section is devoted to one physics application, provided by systems with strong dipolar forces, which have 3 as upper-critical dimension.
The Standard Model (SM) of fundamental interactions
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
The Standard Model (SM) 2020 of weak, electromagnetic and strong interactions, based on gauge symmetry and spontaneous symmetry breaking, describes all known fundamental interactions at the microscopic scale except gravity and, perhaps, interactions with dark matter. The SM model has been tested systematically in collider experiments, and in the case of strong interactions (quantum chromodynamics) also with numerical simulations. With the discovery in 2012 of the Higgs particle at the Large Hadron Collider (LHC) at the European Council for Nuclear Research (CERN), all particles of the SM have been identified, and most parameters have been measured. Still, the Higgs particle remains the most mysterious particle of the SM, since it is responsible for all the parameters of the SM except gauge couplings and since it leads to the fine-tuning problem. The discovery of its origin, and the precise study of its properties should be, in the future, one of the most important field of research in particle physics. Since we know now that the neutrinos have masses, the simplest extension of the SM implies Dirac neutrinos. With such a minimal modification, consistent so far (2020) with experimental data, the lepton and quark sectors have analogous structures: the lepton sector involves a mixing matrix, like the quark sector (three angles have been determined, the fourth charge conjugation parity (CP) violating angle is still unknown).
Lattice gauge theories: Introduction
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
Lattice gauge theories are based on the notion of parallel transport. They can be considered as non-perturbative regularizations of the continuum gauge theories in the sense of a low-temperature expansion. The chapter is mainly devoted on a study of matterless lattice gauge theories from the point of view of phase transitions. This means many properties of a realistic theory like quantum chromodynamics (QC) cannot be investigated, but the important question of confinement can still be studied: does the theory generate a force between charged particles increasing at large distances, so that heavy quarks in the fundamental representation cannot be separated? More generally, can one find charged asymptotic states like massless vector particles in the theory? Lattice gauge theories have properties quite different from the ferromagnetic systems. In particular the absence of a local order parameter requires a study of the behaviour of a non-local quantity, a functional of loops generally called Wilson's loop, to distinguish between the confined and deconfined phases, characterized by an area or perimeter law, respectively.
Elements of classical and quantum gravity
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
This chapter has two purposes; to describe a few elements of differential geometry that are required in different places in this work, and to provide, for completeness, a short introduction to general relativity (GR) and the problem of its quantization. A few concepts related to reparametrization (more accurately, diffeomorphism) of Riemannian manifolds, like parallel transport, affine connection, or curvature, are recalled. To define fermions on Riemannian manifolds, additional mathematical objects are required, the vielbein and the spin connection. Einstein–Hilbert's action for classical gravity GR is defined and the field equations derived. Some formal aspects of the quantization of GR, following the lines of the quantization of non-Abelian gauge theories, are described. Because GR is not renormalizable in four dimensions (even in its extended forms like supersymmetric gravity), at present time, a reasonable assumption is that GR is the low-energy, large-distance remnant of a more complete theory that probably no longer has the form of a quantum field theory (QFT) (strings, non-commutative geometry?). In the terminology of critical phenomena, GR belongs to the class of irrelevant interactions: due to the presence of the massless graviton, GR can be compared with an interacting theory of Goldstone modes at low temperature, in the ordered phase. The scale of this new physics seems to be of the order of 1019 GeV (Planck's mass). Still, because the equations of GR follow from varying Einstein–Hilbert action, some regularized form is expected to be relevant to quantum gravity. In the framework of GR, the presence of a cosmological constant, generated by the quantum vacuum energy, is expected, but it is extremely difficult to account for its extremely small, measured value.
Generalized non-linear σ-models in two dimensions
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
This chapter describes the formal properties, and discusses the renormalization, of quantum field theories (QFT) based on homogeneous spaces: coset spaces of the form G/H, where G is a compact Lie group and H a Lie subgroup. In physics, they appear naturally in the case of spontaneous symmetry breaking, and describe the interaction between Goldstone modes. Homogeneous spaces are associated with non-linear realizations of group representations. There exist natural ways to embed these manifolds in flat Euclidean spaces, spaces in which the symmetry group acts linearly. As in the example of the non-linear σ-model, this embedding is first used, because the renormalization properties are simpler, and the physical interpretation of the more direct correlation functions. Then, in a generic parametrization, the renormalization problem is solved by the introduction of a Becchi–Rouet–Stora–Tyutin (BRST)-like symmetry with anticommuting (Grassmann) parameters, which also plays an essential role in quantized gauge theories. The more specific properties of models corresponding to a special class of homogeneous spaces, symmetric spaces (like the non-linear σ-model), are studied. These models are characterized by the uniqueness of the metric and thus, of the classical action. In two dimensions, from the classical field equations an infinite number of non-local conservation laws can be derived. The field and the unique coupling renormalization group (RG) functions are calculated at one-loop order, in two dimensions, and shown to imply asymptotic freedom.
Instantons in quantum mechanics (QM)
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
Perturbative expansion can be generated by calculating Euclidean functional integrals by the steepest descent method always looking, in the absence of external sources, for saddle points in the form of constant solutions to the classical field equations. However, classical field equations may have non-constant solutions. In Euclidean stable field theories, non-constant solutions have always a larger action than minimal constant solutions, because the gradient term gives an additional positive contribution. The non-constant solutions whose action is finite, are called instanton solutions and are the saddle points relevant for a calculation, by the steepest descent method, of barrier penetration effects. This chapter is devoted to simple examples of non-relativistic quantum mechanics (QM), where instanton calculus is an alternative to the semi-classical Wentzel–Kramers–Brillouin (WKB) method. The role of instantons in some metastable systems in QM is explained. In particular, instantons determine the decay rate of metastable states in the semi-classical limit initially confined in a relative minimum of a potential and decaying through barrier penetration. The contributions of instantons at leading order for the quartic anharmonic oscillator with negative coupling are calculate explicitly. The method is generalized to a large class of analytic potentials, and explicit expressions, at leading order, for one-dimensional systems are obtained.
Multi-instantons in quantum mechanics (QM)
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
In general, a linear combination of instanton solutions is not a solution of the imaginary-time equations of motion, because the equations not linear. Moreover, in quantum mechanics (QM), all solutions of the classical equations can depend only on one time collective coordinate (in this respect, in field theory, the situation is different). However, a linear combination of largely separated instantons (a multi-instanton configuration) renders the action almost stationary, because each instanton solution differs, at large distances, from a constant solution by only exponentially small corrections (in field theory this is only true if the theory is massive). A situation where multi-instantons play a role is provided by large order behaviour estimates of perturbation theory for potentials with degenerate minima. When one starts from a situation in which the minima are almost degenerate, one obtains, in the degenerate limit, a contribution of the superposition of two, infinitely separated, instantons, but with an infinite multiplicative coefficient. Indeed, in this limit, the fluctuations which tend to change the distance between the instanton and the anti-instanton induce a vanishingly small variation of the action. To correctly determine the limit, one has to introduce a second collective coordinate which describes these fluctuations. The determination, at leading order, of all many-instanton contributions has led to conjecture the exact form of the semi-classical expansion for potentials with degenerate minima, generalizing the exact Bohr-Sommerfeld quantization condition.
Popular Rewritings of theOrlando Furiosoas Forms of Criticism
Authors: Lucioli Francesco 
Published: June 2021

AbstractEditions, paratextual apparatuses, translations, theoretical treatises, and dialogues influenced the critical debate about Ariosto’s Orlando furioso, and rapidly became the main route to its canonization. However, immediately after its publication, the Furioso also catalysed the production of new literary texts, which aimed to offer rewritings of and critical insights into the poem. This chapter focuses on this specific form of creative reception, thus far neglected in scholarly studies of Ariosto. It aims to highlight some of the critical readings and interpretations of the Furioso that such popular pamphlets offered to a wide readership in early modern Italy. It reveals a strong continuity across critical commentaries and rewritings of the poem. Both interpretations and adaptations of the Furioso reveal a commitment to pursuing contemporary cultural debates, for instance about the nature of women, influenced by Ariosto and his words: there is a dialogue between popular rewritings and erudite readings of the poem.
The Play in the Mind’s Eye
Authors: Hutson Lorna 
Published: June 2021

AbstractAnglophone criticism of English Renaissance drama largely assumes the irrelevance of sixteenth-century continental critical debates on how to achieve verisimilitude. This chapter argues that English dramatists’ rejection of the Aristotelian unities was not in itself a solution to the problems of making theatre imaginatively compelling: all the challenges discussed by Italian critics were also challenges for English dramatists. Their plays manipulate what we might call the ‘unscene’, whereby the audience infers and imagines characters’ past histories, motives, offstage locations, and inner lives. Shakespeare and other dramatists invite us to supplement and make sense of what we actually see onstage by their use of the topics of ‘circumstance’: topics of time, place, cause, and manner which, in the period’s rhetorical and dialectical traditions, were used to give narratives and descriptions an imaginative liveliness known as enargeia or evidentia. This account is supported by the contemporary critical witness of William Scott.
Extended Cognition and The Innovation Process
Authors: Mastrogiorgio Antonio , Petracca Enrico , Palumbo Riccardo 
Published: June 2021

Abstract
Innovations advance into the ‘adjacent possible’, enabled and constrained by the current state of the world, in a way that is unpredictable and not law-entailed. Unpredictability is the hallmark of the idea that innovation processes are contingent and embodied in the interaction between individuals and artefacts in the environment. In this chapter, we explore the cognitive and behavioural factors involved in exaptive innovation processes by using the notion of ‘extended cognition’. Extended cognition builds on the hypothesis that cognitive processes are not limited to the brain but also extend into the physical world as the objects of the environment facilitate, integrate with, and even constitute specific cognitive processes. We argue that exaptive innovations can be better understood by focusing on practicality and procedural knowledge from an extended cognition perspective. Artefact manipulation is not merely pragmatic but also epistemic as it enables specific reasoning processes that lead to the discovery of new uses.
Manganites
Authors: Kresin Vladimir Z. , Ovchinnikov Sergei G. , Wolf Stuart A. 
Published: June 2021

Abstract
This chapter focuses on manganites. There is a large similarity between the two families of mixed-valence compounds, the cuprates and the manganites. However, manganites display colossal magnetoresistance. The most fundamental property of manganites is the strong correlation between their transport properties and their magnetic properties. This correlation is caused by the double-exchange mechanism. The Hund interaction and the Jahn–Teller effect are the key ingredients of the microscopic theory. The transition to the ferromagnetic and metallic state is of a percolative nature. The superconducting–antiferromagnetic–superconducting Josephson junction is described. One can observe giant oscillations of the Josephson current as a function of a weak external magnetic field. The main properties, including the electron–hole asymmetry can be described in the framework of a generalised two-band picture. A peculiar isotope effect can be observed.
Superconducting States in Nature
Authors: Kresin Vladimir Z. , Ovchinnikov Sergei G. , Wolf Stuart A. 
Published: June 2021

Abstract
This chapter discusses superconducting states in nature. The absence of resistance is the most remarkable manifestation of the superconducting state. But pair correlation is a general phenomenon that can be manifested in various systems, such as atomic nuclei, where the pairing is manifested in spectra, especially via the odd–even effect (the presence of unpaired nucleons makes it possible for nuclei to absorb a lower frequency of radiation than nuclei with an even number of nucleons can) and in the amplitudes of their momenta of inertia, which are smaller than in a rigid model. Another system, the neutron star, has an entirely different spatial scale. However, its low heat capacity leads to its rapid cooling, and the existence of a vortex structure affects the star’s rotation period. Finally, biologically active systems contain delocalised electrons, and the formation of electron pairs affects charge transfer, which is similar to Josephson tunnelling.
Britain’s European Island-Empire, 1793–1815
Authors: Davey James 
Published: June 2021

Abstract
This chapter explores the creation and maintenance of Britain’s European island empire during the wars against Revolutionary and Napoleonic France. It traces the initial establishment of island bases in the Mediterranean, North and Baltic Seas, outlining their importance to British trade and strategy. It explains how and why British war aims came to rely on these imperial possessions. Across the Mediterranean, the war came to be defined by the extension of island empires. British victory in 1814 owed much to these islands, lynchpins of its wider European strategy. In northern waters, the island of Heligoland acted as a rendezvous point for trade with the continent, and was a key site from which Napoleon’s ‘Continental System’ could be undermined. Britain’s European island empire proved itself to be a crucial part of Britain’s wider imperial network, and its significance would continue into the nineteenth century and the era of Pax Britannica.
‘Sailing on the same uncertain sea’
Authors: Hamilton Douglas 
Published: June 2021

Abstract
Although they were small, the islands of the Caribbean were central rather than peripheral to the idea of empire. By the seventeenth century, the islands of the Antillean archipelago were already integral to European imperial rivalry and—as a result—came to shape European notions of what empires were and what they were for. This chapter explores the shifting nature of these islands as they emerged to become imperial powerhouses in the eighteenth century. This transformation was set against the backdrop of the great upheavals of war and revolution. The shifting demography of the West Indies and their economic and strategic importance exposed them particularly to the threats created by the geopolitical maelstrom around them. This chapter argues that their island nature intensified how they were affected by, and responded to, the profound and unprecedented uncertainties of the Age of Revolutions.
Desires and Reasons
Authors: Gregory Alex 
Published: June 2021

AbstractThis chapter explores subjectivism, the view that all reasons have their source in desire. It first rehearses two classic objections to subjectivism: it has implausible implications about which reasons people have, and about what good deliberation looks like. The chapter then offers some reasons to think that objectivism, especially when combined with desire-as-belief, can explain away the appeal of subjectivism. Most centrally, we should make a clear distinction between rational requirements and non-rational requirements, and then say that our desires make a difference only to what it is rational to do. The chapter ends by offering some reasons to doubt desire-based theories of wellbeing, which would also fit poorly with desire-as-belief.
Building a Conservative Welfare State in Botswana
Authors: Seekings Jeremy 
Published: June 2021

Abstract
Of the African countries that initiated social assistance programmes prior to the 2000s, Botswana stands out in that its policy-making was not the result of settler or immigrant populations. Reforms in Botswana stemmed instead from the imperatives of drought relief in an agrarian society, fuelled by the ruling party’s concern first to establish the authority and legitimacy of the post-colonial state and then to ensure re-election in the face of electoral competition from opposition parties. State-building was made possible also by extraordinary economic growth. The result was a system of social assistance that covered a large part of the population but was also distinctively conservative in terms of the value of benefits, a preference for in-kind over cash transfers, and the prioritization of workfare. Botswana’s path to social assistance prefigured the path followed by many other African countries in the 2000s.
The Politics of Promoting Social Cash Transfers in Zambia
Authors: Pruce Kate , Hickey Sam 
Published: June 2021

Abstract
This chapter examines the rise of social cash transfers in Zambia, going beyond the focus on elections and institutions within mainstream accounts of how social protection is likely to emerge in Africa to demonstrate that there are two alternative drivers: shifting dynamics within Zambia’s political settlement and the promotional efforts of a transnational policy coalition. The extensive efforts of this policy coalition helped get social cash transfers onto the policy agenda, but they only gained political traction when the balance of power within Zambia’s ruling coalition shifted and key actors perceived there to be a crisis regarding the distributional strategies deployed to maintain the stability and legitimacy of the political settlement. Social protection has yet to displace existing interests, ideas, and rent-allocation practices; however, cash transfers are gaining localized support. What matters now is the way in which such transfers become integrated within Zambia’s distributional regime.
The Politics of Promoting Social Protection in Uganda
Authors: Bukenya Badru , Hickey Sam 
Published: June 2021

Abstract
The success of efforts to promote social protection in Uganda since the early 2000s has varied considerably, with cash transfers progressing much further than social health insurance. Using original primary research and a process-tracing methodology, we show that external actors were able to form a coherent policy coalition around cast transfers and promote them in ways that became aligned with the dominant ideas and incentives of powerful actors within Uganda’s political settlement. In contrast, proponents of health insurance struggled to mobilize a coalition capable of overcoming actors with greater holding power, particularly the President and private sector actors. Whereas ‘just giving money to the poor’ fits with Uganda’s increasingly personalized-populist political settlement, the hard work of building a credible health system, and formally requiring citizens to contribute to their own healthcare, requires a commitment and capacity to promoting a new social contract that seems to be lacking in Uganda.