bluuebunny/crossref_metadata_2025_split huggingface dataset:
Black Holes
Authors: D'eath P D 
Published: November 2023

Abstract
One of the major applications of general relativity is to the study of black holes formed by the gravitational collapse of a massive body (Misner et al. 1973) or in the early universe by the collapse or collision at high speeds of regions containing large amounts of energy (Barrow and Carr 1978). Black holes are an intrinsically non-linear phenomenon, depending on the strong-field behaviour of the gravitational field. In a black hole, the gravitational field is so strong that even light cannot escape. Black holes should be contrasted with another generic feature of the vacuum gravitational field-gravitational waves. There one solves approximately linear perturbation equations, perhaps about a nontrivial background space-time, to describe the waves. Indeed, at least in the noncosmological case, one might conjecture that a generic vacuum gravitational field could be built up by ‘superposing’ in a non-linear way the fields of various black holes and gravitational radiation. This superposition is described in Chapters 3 and 4. One can also extend this to the case in which there is matter in the space-time.
The Homotopy Category of (n − 1)-Connected (n + 1)-Types
Authors: Baues Hans-Joachim 
Published: November 2023

Abstract
We have to consider the hierarchy of categories and functors (n≥ 2) where types is the full category of (n -−1)-connected (n + k)-types, that is, of CW-spaces Y with πiY = 0 for i &lt; n and i &gt; n + k. The functor P is the Postnikov functor which carries an (n + k)-type to its (n + k − 1)-type, k ≥l. Since (n -−1)-connected n-types are the same as Eilenberg–Mac Lane spaces K(A, n), we can identify them with abelian groups.
Decomposition of Homotopy Types
Authors: Baues Hans-Joachim 
Published: November 2023

Abstract
In this chapter we describe explicit results on the classification of homotopy types. For example we give a complete list of (n -−1)-connected (n + 3)dimensional homotopy types X, n≥ 4, for which all homology groups Hi(X) are cyclic. We also obtain a complete list of all homotopy types X for which πn X, πn+ 1 X, πn+2 X, nɥ 4, are cyclic groups and for which π i X is trivial otherwise. These results are obtained by describing the corresponding indecomposable homotopy types. The indecomposable (n − 1)-connected (n + 3)dimensional polyhedra were found in Baues and Hennes [HC]. The complete solutions of classification problems in this chapter show that the prospect of homotopy types is not so dim.
Homotopy Groups in Dimension 4
Authors: Baues Hans-Joachim 
Published: November 2023

Abstract
The computation of the homotopy groups πn X, n≥ l, of a connected space X is a fundamental problem of algebraic topology. It is well known how to determine the fundamental group πnX in terms of the attaching maps of 2-cells in X. For n ≥2 we may assume that X is simply connected since πn X coincides with the corresponding homotopy group of the universal cover of X.
Dual spaces and the Hahn-Banach theorem
Authors: Meise Reinhold , Vogt Dietmar 
Published: November 2023

Abstract
The elements of E ′are called continuous linear forms or continuous linear functionals on E. In this chapter we will show that for every normed space E, the space E′ is so plentiful that E′ can be used to investigate properties of E. The richness of E′ results from the Hahn-Banach theorem which will be proved with the help of Zorn’s lemma.
Matroids
Authors: Oxley James 
Published: November 2023

Abstract
A matroid consists of a collection of subsets of a finite set which, loosely speaking, behave like the edge sets of cycles in a graph. Matroids also arise naturally from matrices and projective geometries. This chapter provides some examples, mainly in the context of connectivity, of how the interplay between graphs and matroids has led to new results for both matroids and graphs. Matroids were introduced by Hassler Whitney [22] in 1935, with the aim of capturing the fundamental properties of dependence that are common to graphs and matrices.
Basic point set topology
Authors: Lawson Terry 
Published: November 2023

Abstract
We will also discuss more precisely the “geometrical objects” in which we are interested (called topological spaces), but our viewpoint will primarily be to understand more familiar spaces better (such as surfaces) rather than to explore the full generalities of topological spaces. In fact, all of the spaces we will be interested in exist as subspaces of some Euclidean space Rn. One of the methods of mathematics is to abstract central ideas from many examples and then study the abstract concept by itself. Although it often seems to the student that such an abstraction is hard to relate to in that we are frequently disregarding important information of the particular examples we have in mind, the technique has been very successful in mathematics. Frequently, the success is rooted in the following idea: knowing less about something limits the avenues of approach available in studying it and this makes it easier to prove theorems (if they are true). Of course, the measure of the success of the abstracted idea and the definitions it suggests is frequently whether the facts we can prove are useful back in the specific situations which led us to abstract the idea in the first place. Some of the most important contributions to mathematics have been made by those who have figured out good definitions. This is difficult for the student to appreciate since definitions are usually presented as if they came from some supreme being. It is more likely that they have evolved through many wrong guesses and that what is presented is what has survived the test of time.
The Gibbs formulation
Authors: Carrington Gerald 
Published: November 2023

Abstract
We shall initially consider only simple systems, which we identify as follows. First, a simple system is homogeneous, having no internal walls or partitions. Second, we assume that its equilibrium state is identified by the value of U, the amount of each of its chemical components, expressed as mol numbers, N1, N2, … , Nr and the deformation variables for the system.
Symmetry in Physical Laws
Authors: Brink D M , Satchler G R 
Published: November 2023

Abstract
A THEORETICAL investigation of a physical problem may come upon difficulties of two kinds. The exact physical laws govern¬ing the behaviour of a system may not be known, making it impossible to arrive at a complete theoretical description of the system. Problems of fundamental particle structure and reactions present this first difficulty in an acute form. More often the situation is analogous to that encountered in prob¬lems of atomic and molecular structure, where the inter¬ actions (Coulomb forces) are well-known, but where the struc ture in a particular problem may be so complicated that no exact solution can be found.
Tensors and Tensor Operators
Authors: Brink D M , Satchler G R 
Published: November 2023

Abstract
WE are accustomed to deal with certain physical quantities such as mass and energy which are in no way connected with the orientation of our coordinate system and which have no directional properties. Such quantities a.re sea.la.rs, or tensors of rank zero. ‡ Other quantities, such as the position of a point in space or the velocity of a particle, have associated with them a direc¬tion as well as a magnitude. These quantities are vectors or tensors of rank one and in order to specify them we must give the direction as well as the magnitude.
Matrix Elements of Tensor Operators
Authors: Brink D M , Satchler G R 
Published: November 2023

Abstract
WE are now in a position to calculate those parts of any physical problem which are concerned with angular integrations, the coupling of angular momentum vectors, or our choice of coordinate system-in fact general rotational symmetries-which we might call the ‘geometrical’ parts. The basic technique is to exploit the simplest matrix reduction which we have, already met in Chapter IV, namely the WignerEckart theorem for the matrix elements of spherical tensors.
Dynamics of Heavy Electrons
Authors: Kuramoto Y , Kitaoka Y 
Published: November 2023

Abstract
Heavy electrons are found among a number of lanthanide and actinide compounds, and are characterized by a large effective mass which becomes comparable to the mass of a muon. Heavy electrons exhibit rich phenomena such as unconventional superconductivity, weak anti- ferromagnetism, or pseudo meta-magnetism. This book is intended not only as a monograph, but can readily serve as an advanced textbook on theoretical and experimental physics of strongly correlated electrons. Over the last two decades, heavy electrons have been the focus of very active experimental and theoretical studies. Many established ideas and techniques have been insufficient to describe and understand heavy electrons and their impact properly. On the theoretical side, quantum fluctuations make mean-field theories difficult to handle, while on the experimental side, extreme conditions such as strong magnetic fields and pressure at ultra-low temperatures may be required. Heavy electron systems as described in this book offer a case study for applying and testing most of the major tools in theoretical and experimental condensed matter physics. Graduate students and researchers working on strongly correlated condensed matter systems will find in this book a comprehensive introduction and many examples how conventional concepts of solids may work or not work, and how they can be refined and sharpened in the context of heavy electron systems.
Preface
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
Nuclear physics with electromagnetic probes has its roots deep in the early years of modem physics. Soon after the discovery of the Dirac (1928) equation for the relativistic electron, Mott (1929) derived the cross-sectional formula for the scattering of Dirac particles by point nuclei. Just two years after the discovery of the neutron by Chadwick (1932), which indicated the composite nature of nuclei in terms of nucleons, the photodisintegration of the deuteron by Chadwick and Goldhaber (1934) may be considered the first photonuclear experiment.
The Electromagnetic Interaction
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
In this introductory chapter we give the basic formalism to describe the electromagnetic field and its interaction with hadronic matter for both real and virtual photons. The formalism is developed for the use of an electromagnetic probe to investigate the single-particle (s.p.) properties of atomic nuclei and to study the many-body effects which are particularly important in nuclear structure. A number of formulae will be found in this chapter: they will be useful in the treatment of the problems discussed in all sections of the book. Moreover, they will give a general framework suitable for providing a clear starting point to understand the different situations one has to face when working in the field and to find the appropriate solutions. After a brief reminder of the general properties of the electromagnetic field, with particular attention to the gauge invariance of the electromagnetic potential, the one-photon exchange approximation is discussed for electron scattering. This approximation is the fundamental basis of the whole treatment and essentially relies upon the relative weakless of the electric force. In the few cases where a better approximation is necessary, specific sections will be devoted to these refinements. Attention will be focused on the longitudinal and transverse components of the electromagnetic interaction with respect to the momentum transfer q, since a clear comparison between the electron and the photon probe can be made in this way. Moreover, in different situations this separation produces several observable quantities that can clarify some aspects of the reaction mechanism or of nuclear structure, which are averaged and therefore obscured in the global response.
Form Factors of Excited Baryons
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
The finding that the nucleon is an extended object (Hofstadter and McAllister 1955; Chambers and Hofstadter 1956; Hofstadter 1956) with an internal structure (Bloom et al. 1969; Breidenbach et al. 1969; Miller et al. 1972; Friedman and Kendall 1972) immediately calls for an understanding of its excitation spectrum. The excitation spectrum of the nucleon has been extensively studied by pion scattering and a large number of states have been discovered after the pioneering work of Fermi and coworkers (Anderson et al. 1952). Baryon states are classified by the Particle Data Group (Montanet et al. 1994) according to a quark model based on SU(6) spin-flavour symmetry. The structure and dynamics of hadrons have to be understood in terms of a theoretical description of strong interactions ultimately derived from QCD, but in a regime where the underlying QCD dynamics cannot be treated perturbatively. Thus the complexity of hadrons requires the development of soluble models not only retaining the basic symmetries of QCD but at the same time also containing the relevant dynamical features of interacting quarks and gluons. The electromagnetic excitation of nucleon resonances (N*) gives important complementary information on the internal dynamics of baryons since it provides constraints on theoretical models by determining the photocoupling amplitudes associated with the-γNN* vertex at different four-momentum transfers Q2•
One-Nucleon Knockout Reactions
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

abstract
This chapter is devoted to the analysis of the experimental data of direct knockout reactions with one-nucleon emission. The interest will be addressed mainly to complex nuclei, without considering, in general, the few-body systems. A choice of the available data will be presented, in order to provide a review of typical transitions and to stress the mechanism and the fundamental properties of the process. Attention will be focused on the reactions where the residual nucleus is left in a discrete state. The energy region above the two-nucleon emission threshold will be treated in Chapter 8. The one-particle mechanism, presented and discussed in the preceding chapter, reproduces very well the experimental data of one-nucleon knockout from valence states. This is due to the relatively weak electromagnetic interaction and to the fact that electron scattering can transfer a rather low energy combined with a large momentum, which favours the direct interaction with a single nucleon.
Spin Degrees of Freedom
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
Polarization experiments are a rich and unique source of information on the nuclear response (Wolfenstein 1956; Davydov 1958; Simonius 1974; Pal 1983). Indeed, only measurements of polarization observables allow a complete determination of transition amplitudes and therefore give all the information on the response of the system. In general these measurements depend on a larger number of observables, which are hidden in the unpolarized case, where sums and/or averages over spin states are performed. Some of the polarization observables are expected to be sensitive to small components of the transition amplitude which cannot be extracted without ambiguity from the unpolarized cross section. Therefore, their determination would impose severe constraints on theoretical models and so are of great interest. Unfortunately, experiments with polarized targets have to face the difficulty of maintaining polarization in external cryogenic targets or of constructing polarized jet targets with sufficiently high density, while the measurements of recoil polarization are performed with polarimeters which need a double scattering. Therefore only few results are at present available and a complete determination of the transition amplitudes represents an ambitious programme. However, a large number of polarization measurements will be carried out in the future when new facilities and improved experimental techniques are available.
Polarization Experiments
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
In the past, spin degrees of freedom were seldom considered in studies of electromagnetic interactions with hadrons. The inclusion of the spin physics in experiments with electromagnetic probes was hampered by several technical difficulties which are now partly overcome. Two major advances have been made concerning polarized beams. On the one hand, monochromatic beams of linearly and circularly polarized real photons are obtained by backward scattering of high-energy electrons on a laser beam. This technique was developed by the LADON collaboration in Frascati and is now also used at Brookhaven by the LEGS collaboration with photon energies up to about 350 MeV. With the GRAAL facility in Grenoble investigation at higher photon energies will be possible. On the other hand, reliable high-current polarized electron sources are now available as a result of hard work over more than 20 years. The first polarized electron beams for intermediate-energy physics are operating at MIT-Bates and Mainz. Other beams will soon be ready at NIKHEF and CEBAF.
Electrons at Crystal Surfaces
Authors: Davison Sydney G , Stęślicka Maria 
Published: November 2023

Abstract
Since crystals in their natural state are finite, i.e., limited by surfaces, the question arises as to how the energy spectrum of an electron propagating in a finite crystal differs from that in an infinite one. The partial answer is provided by using the Born-von K árm án (1912, 1913) boundary condition (2.138), which shows that, if a finite crystal of N atoms is cut from an infinite one, then the previous continuous allowed band becomes a sequence of N discrete levels (2.141). Clearly, this is not a big difference, if the crystal (i.e., N) is very large. However, there is another important consequence of taking the crystal size into account, namely, that the presence of the surface produces discrete energy levels, which lie in the FEG regions that are inaccessible to electrons in infinite crystals. Tamm (1932) was the first to demonstrate the existence of these surface states by terminating the KP potential as a means of representing the surface. Because of the importance of Tamm’s work in establishing the new idea of surface states, we shall now briefly discuss his findings.
Tight-Binding Approximation
Authors: Davison Sydney G , Stęślicka Maria 
Published: November 2023

Abstract
In the previous chapter, surface states were analysed by means of a potential approach, which is a method that has been developed mainly by physicists. However, the tight-binding approximation (TBA) is based on the electron¬ orbital concept (§2.3), which, while commonly used in solid-state theory, has its origins in quantum chemistry.
Charge Exchange and the Theory of Ion-Atom Collisions
Authors: Bransden B H , McDowell M R C 
Published: November 2023

Abstract
During the last two decades the theory of ion-atom collisons, and particularly of charge-exchange reactions has advanced rapidly to the point where existing texts are no longer suitable as an introduction to the subject. This book aims to remedy the situation by providing an account of modern theoretical methods used to study the interaction of positive ions with atoms (or ions), concentrating particularly on charge exchange reactions. These reactions cannot be studied in isolation, and it is necessary to consider, to some extent, the whole range of ion-atom collisions leading to elastic scattering, excitation, and ionization. The material is presented at a level suitable for beginning research students and is self-contained, but assumes a knowledge of undergraduate quantum mechanics and atomic physics. It should also be useful for experimentalists who wish to assess the status of theoretical treatments of those collision processes in which they are interested.
Anxiety Disorders
Authors: Leahy Robert L , McGinn Lata K , Busch Fredric N , Milrod Barbara L 
Published: November 2023

Abstract
Anxiety disorders are one of the most common psychological disorders found in national surveys of the prevalence of psychiatric problems. Many anxiety disorders are persistent rather than episodic, with a large percentage of patients with generalized anxiety, social anxiety disorder (SAD), or obsessive–compulsive disorder (OCD) reporting difficultiess lasting years.
Psychotherapy For Avoidant Personality Disorder
Authors: Newman Cory F , Fingerhut Randy 
Published: November 2023

Abstract
The diagnostic category of avoidant personality disorder (AvPD) is among those Axis II disorders classified informally as the ‘anxious and fearful’ subgroup (DSM–IV; American Psychiatric Association, 1994, see Box 26.1 for standardized criteria), and is one of the more prevalent forms of personality pathology (Ekselius et al., 2001; Alden et al., 2002).
Psychotherapy of Obsessive–Compulsive Personality Disorder
Authors: Gabbard Glen O , Newman Cory F 
Published: November 2023

Abstract
The symptoms of obsessive–compulsive personality disorder (OCPD) are well described in the DSM–IV (Diagnostic and statistical manual for mental disorders, 4th edn) classification (see Table 28.1). Most of the symptoms can be regarded as lifelong adaptations that frequently do not create a great deal of distress for the patient. Certain aspects of the condition are even adaptive, such as an emphasis on detail, work, and achievement.
Psychotherapy Supervision
Authors: Lomax James W , Andrews Linda B , Burruss John W , Moorey Stirling 
Published: November 2023

Abstract
This chapter explores individual supervision as a unique educational structure for psychotherapy education. Such supervision is of paramount importance in the professional formation of the psychotherapist in particular, but it is also important for all mental health practitioners regardless of whether psychotherapy plays a significant role on their professional lives or not (Mohl et al., 1990).
Perturbation theory and Feynman diagrams
Authors: Maggiore Michele 
Published: November 2023

Abstract
In Chapter 4 we studied the quantization of free fields. We now introduce the interaction. In the canonical quantization, perturbation theory is developed more easily using the Hamiltonian formalism (the Lagrangian formalism is instead more useful in the path integral quantization that will be discussed in Chapter 9). We therefore consider a general field theory with a Hamiltonian where Ho is the free Hamiltonian and Hint is the interaction term. The interaction term will be considered small. For instance in QED as discussed in Section 3.5.4. (Note that the identity Hint = -Lint holds only when the interaction Lagrangian does not contain derivatives of the fields.) The smallness of the interaction follows from the fact that the parameter which turns out to be relevant for the perturbative expansion is a= (e /41r) 1/137.
Path integral quantization
Authors: Maggiore Michele 
Published: November 2023

Abstract
Until now we have used canonical quantization, that is, we have promoted the classical fields to quantum operators. In this chapter we present an alternative formulation of quantum mechanics and of QFT, due to Feynman (who elaborated on work of Dirac) and known as path integral quantization, in which the coordinates in quantum mechanics (QM), and the fields in QFT, remain ordinary functions rather than operators.