bluuebunny/crossref_metadata_2025_split huggingface dataset:
Stomach and duodenal disorders
Authors: McGregor Colleen 
Published: June 2021

Abstract
This chapter covers core curriculum topics relating to benign and malignant conditions of the stomach and duodenum. Particular focus is given to the diagnostic approach to and therapeutic management of Helicobacter pylori infection and peptic ulcer disease. Other benign conditions covered include gastroparesis and duodenal adenomas, namely the investigation and management thereof. Attention is given to the identification of and management of GISTs, pre-malignant gastric lesions, gastric dysplasia and gastric polyps. Also importantly covered are the epidemiology, presentation, investigation and treatment of gastric adenocarcinoma. Finally, a selection of questions covers the rare presentations of neuroendocrine tumours, Ménétrier’s disease and Zollinger-Ellison syndrome.
Small intestinal disorders
Authors: Ambrose Tim 
Published: June 2021

AbstractThis chapter covers core curriculum topics relating to small intestinal disorders and malabsorption. This includes a discussion of key gut hormones involved in digestion and absorptive processes including with relevance for obesity. Questions on gastrointestinal neurotransmitters and transporters provide education in gut physiology. The protean presentations of several micronutrient deficiencies seen in clinical practice are discussed. Focus is given to the diagnosis, initial management and follow up of patients with coeliac disease and villous atrophy including later-onset complications such as enteropathy-associated T cell lymphoma. Also covered is the investigation of small intestinal motility disorders and the manifestations and management of functional abdominal conditions such as irritable bowel syndrome. Disorders of bile acid recirculation, microbial dysregulation including through acute infections, and key medications causing presentations with diarrhoea are incorporated in this chapter. Additional curriculum material regarding small intestinal disorders will also be covered in the mock examination chapter.
Gaussian integrals. Algebraic preliminaries
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
In this work, the perturbative aspects of quantum mechanics (QM) and quantum field theory (QFT), to a large extent, are studied with functional (path or field) integrals and functional techniques. This physics textbook thus begins with a discussion of algebraic properties of Gaussian measures, and Gaussian expectation values for a finite number of variables. The important role of Gaussian measures is not unrelated to the central limit theorem of probabilities, although the interesting physics is generally hidden in essential deviations from Gaussian distributions. A few algebraic identities about Gaussian expectation values, in particular Wick's theorem are recalled. Integrals over some type of formally complex conjugate variables, directly relevant for boson systems are defined. Fermion systems require the introduction of Grassmann or exterior algebras, and the corresponding generalization of the notions of differentiation and integration. Both for complex and Grassmann integrals, Gaussian integrals, and Gaussian expectation values are calculated, and generalized Wick's theorems proven. The concepts of generating functions and Legendre transformation are recalled.
Quantum mechanics (QM): Path integrals in phase space
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
In Chapter 2, a path integral representation of the quantum operator e-β H in the case of Hamiltonians H of the separable form p2/2m + V(q) has been constructed. Here, the construction is extended to Hamiltonians that are more general functions of phase space variables. This results in integrals over paths in phase space involving the action expressed in terms of the classical Hamiltonian H(p,q). However, it is shown that, in the general case, the path integral is not completely defined, and this reflects the problem that the classical Hamiltonian does not specify completely the quantum Hamiltonian, due to the problem of ordering quantum operators in products. When the Hamiltonian is a quadratic function of the momentum variables, the integral over momenta is Gaussian and can be performed. In the separable example, the path integral of Chapter 2 is recovered. In the case of the charged particle in a magnetic field a more general form is found, which is ambiguous, since a problem of operator ordering arises, and the ambiguity must be fixed. Hamiltonians that are general quadratic functions provide other important examples, which are analysed thoroughly. Such Hamiltonians appear in the quantization of the motion on Riemannian manifolds. There, the problem of ambiguities is even more severe. The problem is illustrated by the analysis of the quantization of the free motion on the sphere SN−1.
Symmetries, chiral symmetry breaking, and renormalization
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
Most quantum field theories (QFT) of physical interest exhibit symmetries, exact symmetries or symmetries with soft (e.g. linear) breaking. This chapter deals only with linear continuous symmetries corresponding to compact Lie groups. When the bare action has symmetry properties, to preserve the symmetry it is first necessary to find a symmetric regularization. The symmetry properties of the QFT then imply relations between connected correlation functions, and vertex functions, called Ward–Takahashi (WT) identities, which describe the physical consequences of the symmetry. WT identities also constrain UV divergences, and the counter-terms that render the theory finite are not of most general form allowed by power counting. As a consequence the renormalized action is expected to keep some trace of the initial symmetry. Such an analysis is based on a perturbative loop expansion. More generally, some non-trivial relations survive when to the action are added terms that induce a soft breaking of symmetry (i.e. by relevant terms). The specific examples of linear symmetry breaking, and the very important limiting case of spontaneous symmetry breaking, and quadratic symmetry breaking are examined. Finally, as an application, the example of chiral symmetry breaking in low-energy effective models of hadron physics is discussed.
Critical domain: Universality, ε-expansion
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
In Chapter 15, the scaling behaviour of correlation functions at criticality, T = Tc, has been derived. This chapter is devoted to the critical domain, where the correlation length is large with respect to the microscopic scale, but finite. In dimensions d &lt; 4, above Tc, the property of strong scaling is derived: in the critical domain above Tc, all correlation functions, after rescaling, can be expressed in terms of universal correlation functions, in which the scale of distance is provided by the correlation length. However, because the correlation length is singular at Tc, in this formalism, the critical temperature cannot be crossed. Alternatively, one can expand correlation functions in formal power series of the deviation (T −Tc) from the critical temperature, in presence of a magnetic field. The sum of the expansion satisfies renormalization group (RG) equations also valid for T &lt; Tc and in a magnetic field, from which follow scaling properties in the whole critical domain. The universal two-point function can be expanded when T approaches Tc, using the short-distance expansion (SDE). A few terms of the ϵ expansion (ϵ is the deviation from dimension 4) of a few universal quantities are reported. Calculations at fixed dimension and summation of perturbative expansions are described. The conformal bootstrap based on the SDE and conformal invariance at the infrared (IR) fixed point provides an alternative method to determine critical exponents.
Gross–Neveu–Yukawa and Gross–Neveu models
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
In this chapter, a model is considered that can be defined in continuous dimensions, the Gross– Neveu–Yukawa (GNY) model, which involves N Dirac fermions and one scalar field. The model has a continuous U(N) symmetry, and a discrete symmetry, which prevents the addition of a fermion mass term to the action. For a specific value of a coefficient of the action, the model undergoes a continuous phase transition. The broken phase illustrates a mechanism of spontaneous symmetry breaking, leading to spontaneous fermion mass generation like in the Standard Model (SM) of particle physics. In four dimensions, the GNY can be considered as a toy model to represent the interactions between the top quark and the Higgs boson, the heaviest particles of the SM of fundamental interactions, when the gauge fields are omitted. The model is renormalizable in four dimensions and its renormalization group (RG) properties can be studied in d = 4 and d = 4 − ϵ dimensions. A model of self-interacting fermions with the same symmetries and fermion content, the Gross–Neveu (GN) model, has been widely studied. In perturbation theory, for d &gt; 2, it describes only a phase with massless fermions but, in d = 2 + ϵ dimensions, the RG indicates that, at a critical value of the coupling constant, the model experiences a phase transition. In two dimensions, it is renormalizable and exhibits the phenomenon of asymptotic freedom. The massless phase becomes infrared unstable and there is strong evidence that the spectrum corresponds to spontaneous symmetry breaking and fermion mass generation.
O(2) spin model and the Kosterlitz–Thouless’s phase transition
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
At low temperature, the large distance properties of the O(2) spin lattice model can be described by the O(2) non-linear σ-model. The latter model is free and massless in two dimensions. The origin of this peculiarity can be found in the local structure of the field manifold: for N = 2, the O(N) sphere reduces to a circle, which cannot be distinguished locally from a straight line. Because the physical fields are sin θ or cos θ, or equivalently e± iθ, instead of θ, a field renormalization is necessary, and temperature-dependent anomalous dimensions are generated. However, the free θ action cannot describe the long-distance properties of the lattice model for all temperatures, since a high temperature analysis of the corresponding spin model shows that the correlation length is finite at high temperature, and thus a phase transition is required. In fact, it is necessary to take into account the property that θ is a cyclic variable. This condition is irrelevant at low temperature, but when the temperature increases, classical configurations with singularities at isolated points, around which θ varies by a multiple of 2π become important. The action of these configurations (vortices) can be identified with the energy of a neutral Coulomb gas, which exhibits a transition between a low temperature of bound neutral molecules and a high temperature phase of a plasma of free charges. The Coulomb gas can be mapped onto the sine-Gordon (sG) model, mapping in which the low- and high-temperature regions of the models are exchanged. This correspondence helps to understand some properties of the famous Kosterlitz-Thouless (KT) phase transition, which separates an infinite correlation length phase without order, the low-temperature phase of the O(2) spin model, from a finite correlation length phase, the high-temperature phase of the O(2) spin model.
Finite-size effects in field theory. Scaling behaviour
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
A number of numerical calculations, like Monte Carlo or transfer matrix calculations, are performed with systems in which the size in several or all dimensions is finite. To extrapolate the results to the infinite system, it is thus necessary to understand how the infinite size limit is reached. In particular in a system in which the forces are short range, no phase transition can occur in a finite volume, or in a geometry in which the size is infinite only in one dimension. This indicates that the infinite-size extrapolation is somewhat non-trivial. In this chapter, the problem is analysed in the case of second-order phase transitions, in the framework of the N-vector model. The existence of a finite-size scaling is established, extending renormalization group (RG) arguments to this new situation. Then, finite volume geometry and cylindrical geometry, in which the size is finite in all dimensions except one, are distinguished. It is explained how to adapt the methods used in the case of infinite systems to calculate the new universal quantities appearing in finite-size effects, for example, in d = 4−ϵ or d = 2+ϵ dimensions. Special properties of the commonly used periodic boundary conditions are emphasized.
Stochastic differential equations: Langevin, Fokker–Planck (FP) equations
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
This chapter is devoted to the study of Langevin equations, first order in time differential equations, which depend on a random noise, and which belong to a class of stochastic differential equations that describe diffusion processes, or random motion. From a Langevin equation, a Fokker–Planck (FP) equation for the probability distribution of the solutions, at given time, of the Langevin equation can be derived. It is shown that observables averaged over the noise can also be calculated from path integrals, whose integrands define automatically positive measures. The path integrals involve dynamic actions that have automatically a Becchi–Rouet–Stora–Tyutin (BRST) symmetry and, when the driving force derives from a potential, exhibit the simplest form of supersymmetry. In some cases, like Brownian motion on Riemannian manifolds, difficulties appear in the precise definition of stochastic equations, quite similar to the quantization problem encountered in quantum mechanics (QM). Time discretization provides one possible solution to the problem.
Langevin field equations: Properties and renormalization
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
Langevin equations for fields have been proposed to describe the dynamics of critical phenomena, or as an alternative method of quantization, which could be useful in cases where ordinary methods lead to difficulties, like in gauge theories. Some of their general properties will be described here. For a number of problems, in particular related to perturbation theory, it is more convenient to work with an action and a field integral than with the equation directly, because standard methods of quantum field theory (QFT) then become available. For this purpose, one can associate a field integral representation, involving a dynamic action to the Langevin equation. The dynamic action can be interpreted as generated by the Langevin equation, considered as a constraint equation. Quite generally, the integral representation of constraint equations, including stochastic equations, leads to an action that has a Slavnov–Taylor (ST) symmetry and, in a different form, has an anticommuting type Becchi–Rouet–Stora–Tyutin (BRST) symmetry, a symmetry that involves anticommuting parameters. This symmetry has no geometric origin, but is merely a consequence of associating a specific form of integral representations to the constraint equations. This symmetry is used in a number of different examples to prove the renormalizability of non-Abelian gauge theories, or to prove the geometric stability of models defined on homogeneous spaces under renormalization. In this chapter, it is used to prove Ward-Takahashi (WT) identities, and to determine how the Langevin equation renormalizes.
Large order behaviour of perturbation theory
Authors: Zinn-Justin Jean 
Published: June 2021

Abstract
In quantum field theory (QFT), the main analytic tool to calculate physical quantities is the perturbative expansion. Following, Dyson's intuitive argument, the divergence of perturbative series was demonstrated in some models of quantum mechanics (QM) with polynomial potentials, using the Schrödinger equation. Later, it was proposed to study the problem within a path integral formulation. A systematic method in field theory was proposed by Lipatov, using the field integral representation of the φ44 field theory and instantons. It can be shown that the ground-state energy of the quartic anharmonic oscillator is analytic in a cut-plane. The imaginary part of the energy on the cut is related to barrier penetration. The behaviour of the perturbative coefficients at large orders is related to the behaviour of the imaginary part for small and negative coupling and can be obtained by instanton methods. The method has been generalized to the class of potentials for which (in general complex) instanton contributions have been calculated. The same method can be readily applied to boson field theories, while the extension to field theories involving fermions, like Quantum QED, requires additional considerations. The general conclusion is that, in QFT, all perturbative series, expanded in terms of a loop-expansion parameter, are divergent series.
Places of Form in Early Modern Poetics
Authors: Hetherington Michael 
Published: June 2021

Abstract‘Form’ is a notoriously capacious, unreliable, and yet necessary commonplace of both modern and early modern critical vocabulary. This essay explores the flexible and imaginatively generative ways in which the concept migrated from discourses of philosophy and logic into literary criticism and practice, drawing on a range of writers of different nationalities from across the early modern period, but focusing especially on English literature of the Elizabethan fin-de-siècle. It argues, in particular, that one of form’s principal places in that exciting cultural moment was the mind of the poet: the mind trained, structured, or ‘informed’ by poetic theory; the mind as a place which moulds and shapes the materials of language and representation into communicative forms; the mind as the source for the forms of utterance we call ‘style’.
Painting as ‘Reall Performance’ in Rembrandt’s Studio
Authors: Weststeijn Thijs 
Published: June 2021

AbstractWhereas various previous studies have addressed Rembrandt’s own reading habits, this essay shifts attention to the viewer: how did the master expect his public to react to his works? On the basis of art theories from Rembrandt’s circle (chiefly by Samuel van Hoogstraten and Franciscus Junius), the artist’s studio is reconstructed as a place of criticism, where art was evaluated in performative terms: ancient theories of ekphrasis and emotional involvement were put to painterly practice. This practice involved the artist preparing his figure compositions by ‘performing’ in front of a mirror or for an audience, or by trying out small-scale choreographies using dolls. In addition, the presentation of an artwork to viewers could also approach the ideal of an immersion in a virtual reality through the use of curtains, the declamation of texts, and other sound effects.
Introduction
Authors: Kresin Vladimir Z. , Ovchinnikov Sergei G. , Wolf Stuart A. 
Published: June 2021

Abstract
This chapter outlines the story of superconductivity, which started at the beginning of the twentieth century, and describes major breakthroughs, such as the discovery of the Meissner effect and the isotope effect. Several important developments preceded the microscopic theory formulated by Bardeen, Cooper, and Schrieffer: the two-fluid model, London equations, and the Ginzburg–Landau theory. Formulation of the theory brought further progress, such as quasiparticle tunnelling and the Josephson effect, and the search for new mechanisms of superconductivity and novel materials such as high-Tc oxides and hydrides. The main excitations in normal solids, including phonons, polaronic states, plasmons, and magnons, are described. A rigorous description of the adiabatic method, the foundation of the theory of solids, is provided, and the electron–phonon interaction, renormalisation phenomena, and the dynamic polaronic effect are introduced. The Heisenberg model, the key ingredient of the theory of magnetism, is also described.
Mechanisms
Authors: Kresin Vladimir Z. , Ovchinnikov Sergei G. , Wolf Stuart A. 
Published: June 2021

Abstract
This chapter introduces the general concepts of pair correlation, and superconductivity as a strong non-adiabatic phenomenon. Phonon, electronic, and magnetic mechanisms play the major roles; each of them can serve as the origin of the superconducting state. Speaking of the phonon mechanism, it is essential that an explicit expression for Tc depend on the intensity of the electron–phonon interaction. In principle, the electron–phonon mechanism can provide high values of Tc, up to room temperature. Pioneering work by Little, who introduced the electronic mechanism, is described. The mechanism has been analysed for one-dimensional, two-dimensional, and three-dimensional systems. The plasmon mechanism can play a role for layered materials. The superconducting state can be provided by magnetic degrees of freedom. The band limit with spin fluctuations and the regime of strong electron correlations are described. The Hubbard Hamiltonian and the t − J model are the ingredients of the approach.
Inhomogeneous Superconductivity and the ‘Pseudogap’ State of Novel Superconductors
Authors: Kresin Vladimir Z. , Ovchinnikov Sergei G. , Wolf Stuart A. 
Published: June 2021

Abstract
This chapter discusses the high-Tc oxides, which display many unusual properties above Tc, especially for the underdoped compounds. One can observe some features typical for the superconducting state, such as the energy gap, anomalous diamagnetism, and the isotope effect; they coexist with finite resistance. These features are caused by an intrinsic inhomogeneity of the compound. Various energy scales (Tc, Tc*, T*) can be introduced. The system contains a set of superconducting ‘islands’ embedded in a normal metallic matrix. The inhomogeneity is caused by the statistical nature of doping and the pair-breaking effect. The formation of a macroscopic superconducting phase (at T = Tc) corresponds to the transition, which is of a percolative nature. The resistive and Meissner transitions are split. The granular superconductors are inhomogeneous and their properties are similar to those of doped systems. The ordered doping should lead to an increase in the value of the critical temperature.
Britain’s Western Indian Ocean Island-Scape
Authors: Longair Sarah 
Published: June 2021

Abstract
The British Empire had a significant influence on the history of the islands in the western Indian Ocean. In turn, the location, size, culture, and environment of these islands shaped the history of empire. This chapter investigates these islands’ strategic significance, their role in trade and commerce, and their diverse colonial cultures. It also considers these islands as sites of confinement and scientific research. Taken together, this chapter highlights the pivotal role played by western Indian Ocean islands—and their distinctive cultures, environments, and geographies—in the expansion and maintenance of Britain’s maritime empire in the eighteenth and nineteenth centuries.