Books in the SpringerBriefs in Physics series

This concise book reviews methods used for gluing space-time manifolds together. It is therefore relevant to theorists working on branes, walls, domain walls, concepts frequently used in theoretical cosmology, astrophysics, and gravity theory. Nowadays, applications are also in theoretical condensed matter physics where Riemannian geometry appears. The book also reviews the history of matching conditions between two space-time manifolds from the early times of general relativity up to now.

This book provides a comprehensive yet informal introduction to differentiating and integrating real functions with one variable. It also covers basic first-order differential equations and introduces higher-dimensional differentiation and integration. The focus is on significant theoretical proofs, accompanied by illustrative examples for clarity. A comprehensive bibliography aids deeper understanding. The concept of a function's differential is a central theme, relating to the "differential" within integrals. The discussion of indefinite integrals (collections of antiderivatives) precedes definite integrals, naturally connecting the two. The Appendix offers essential math formulas, exercise properties, and an in-depth exploration of continuity and differentiability. Select exercise solutions are provided. This book suits short introductory math courses for novice physics/engineering students. It equips them with vital differentialand integral calculus tools for real-world applications. It is also useful for first-year undergraduates, reinforcing advanced calculus foundations for better Physics comprehension.

This book offers a primer on the fundamentals and applications of the Geroch-Held-Penrose (GHP) calculus, a powerful formalism designed for spacetimes that occur frequently in the teaching of General Relativity. Specifically, the book shows in detail the power of the calculus when dealing with spherically symmetric spacetimes. After introducing the basics, a new look at all the classical spherically symmetric black hole solutions is given within the GHP formalism. This is then employed to give new insights into the Tolman-Oppenheimer-Volkoff equations for stellar structure, including a derivation of new exact anisotropic fluid solutions. Finally, a re-writing of some essential features of black hole thermodynamics within the GHP formalism is performed. The book is based on the authors' lecture notes, used in their undergraduate and graduate lectures and while supervising their upper undergraduate and graduate students. To fully benefit from this concise primer, readers only need an undergraduate background in general relativity.

This book is a set of introductory lecture notes on Conformal Field Theory (CFT). Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. The book starts with a non-perturbative formulation of quantum field theory (Wightman axioms) and then, gradually, focuses on the implications of scale and special conformal symmetry, all the way to the modern conformal bootstrap. This approach includes topics such as subtleties of conformal transformations in Minkowski space-time, the construction of Wightman functions and time-ordered correlators both in position- and momentum-space, unitarity bounds derived from the spectral representation, and the appearance of UV and IR divergences. In each chapter, the reader finds useful exercises to master the subject.This book is meant for graduate students in theoretical physics and for more advanced researchers working in high-energy physics who are not necessarily familiar with the concepts of conformal field theory. Prior knowledge of quantum field theory is needed to master the arguments.

This book is an English translation from a Hungarian book designed for graduate and postgraduate students about the use of variational principles in theoretical physics. Unlike many academic textbooks, it dashes across several lecture disciplines taught in physics courses. It emphasizes and demonstrates the use of the variational technique and philosophy behind the basic laws in mechanics, relativity theory, electromagnetism, and quantum mechanics. The book is meant for advanced students and young researchers in theoretical physics but, also, more experienced researchers can benefit from its reading.

This brief book introduces the Poisson-Boltzmann equation in three chapters that build upon one another, offering a systematic entry to advanced students and researchers. Chapter one formulates the equation and develops the linearized version of Debye-Hückel theory as well as exact solutions to the nonlinear equation in simple geometries and generalizations to higher-order equations. Chapter two introduces the statistical physics approach to the Poisson-Boltzmann equation. It allows the treatment of fluctuation effects, treated in the loop expansion, and in a variational approach. First applications are treated in detail: the problem of the surface tension under the addition of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is developed in modern terms within the loop expansion, and the adsorption of a charged polymer on a like-charged surface within the variational approach. Chapter three finally discusses the extension of Poisson-Boltzmann theory to explicit solvent. This is done in two ways: on the phenomenological level of nonlocal electrostatics and with a statistical physics model that treats the solvent molecules as molecular dipoles. This model is then treated in the mean-field approximation and with the variational method introduced in Chapter two, rounding up the development of the mathematical approaches of Poisson-Boltzmann theory. After studying this book, a graduate student will be able to access the research literature on the Poisson-Boltzmann equation with a solid background.

This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allowscomputation of eigenvalues of quantum mechanical potential problems without solving for thewave function. The examples presented include exotic potentials such as quasi-exactly solvablemodels and Lame an dassociated Lame potentials. A careful application of boundary conditionsoffers an insight into the nature of solutions of several potential models. Advancedundergraduates having knowledge of complex variables and quantum mechanics will find thisas an interesting method to obtain the eigenvalues and eigen-functions. The discussion oncomplex zeros of the wave function gives intriguing new results which are relevant foradvanced students and young researchers. Moreover, a few open problems in research arediscussed as well, which pose a challenge to the mathematically oriented readers.

This book provides a didactic derivation of the main theories of thermotropic and lyotropic liquid crystals, revealing the common molecular-theoretic framework that underpins both theories. This unified context will help young researchers in coming to grips with the basics of the simplest of liquid crystals, being uniaxial nematic liquid crystals, easing them into the intricacies of more complex forms of such materials irrespective of whether they are thermotropic or lyotropic. The coverage provides a theoretical understanding of the phase behaviour, that is, what drives molecules and particles to spontaneously align themselves, as well as an appreciation of the role of entropy, energy and so on. The focus here is on the main theories for the isotropic-nematic transition, being the Maier-Saupe and the Onsager theories, and how they are derived from a common description, known as (classical) density functional theory (DFT). This book will be a valuable resource for senior undergraduate and graduate students, and experimentalists and engineers who feel intimidated by more formal or rigorous theoretical accounts and textbooks. Exercises at the end of each chapter help the reader to apply the basic concepts also to other types of liquid crystal, in particular the smectic liquid crystal.

This book introduces readers to the development of a new generation of high pulse-repetition frequency instruments for multi-dimensional attosecond-resolution photoelectron spectroscopy (attosecond PES). It investigates the power scaling of femtosecond enhancement cavities for efficient intracavity high-harmonics generation (HHG). Further, it derives and verifies advanced resonator designs that feature large illuminated spots on all mirrors, which mitigate both intensity- and thermally-induced enhancement limitations.The dynamics of a high-finesse, passive resonator in the presence of a highly nonlinear optical process such as HHG are quantitatively investigated, both theoretically and experimentally. These investigations are instrumental in achieving the holistic optimization of the XUV source reported on here, which for the first time reached intracavity HHG conversion efficiencies comparable to those achieved in single-pass setups with a similar gas target.Coupling out the XUV beam from the enhancement cavity by purely geometric means, employing both the fundamental and higher-order transverse Gaussian modes, is studied. This offers the advantages of robustness, low distortion to the participating pulses, and photon-energy scalability. Last but not least, the author provides a range of proof-of-principle attosecond angle-resolved PES experiments.The book gives an outlook on the possible future development of cavity-enhanced HHG and an extensive discussion on the generation of isolated XUV attosecond pulses via intracavity wavefront rotation.

This book is a graduate-level self-study guide of bound states in elementary particle physics and consequently in the standard model. The properties of relativistic bound states are discussed for Dirac states, atoms in motion, QED in D=1+1 dimensions, and hadrons in quantum chromodynamics (including color confinement).

This book highlights the first systematic synthesis of various research approaches in forensic medical diagnosis of the morphological and polycrystalline structure of human biological tissues and biological fluids.

The book presents seven fundamental concepts in spacetime physics mostly by following Hermann Minkowski's revolutionary ideas summarized in his 1908 lecture "Space and Time."

This book offers a primer on the fundamental theory of Andreev reflection, a fundamental process in the motion of a Cooper pair, which dominates low-energy electronic transport properties in superconductor junctions including differential conductance and Josephson current.

This book is about the dark photon which is a new gauge boson whose existence has been conjectured. In this book, the authors review the physics of the dark photon from the theoretical and experimental point of view.

The natural generalization of the quantum-mechanical N-particle wave function to relativistic space-time is a function of N space-time points, and thus of N time variables.

In this book, the author addresses selected topics in quantum mechanics that are not usually covered in books, but which are very helpful in developing a student's interest in, and a deeper understanding of the subject. The topics include two different ways of looking at quantum mechanics;

The field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems.

This book presents an overview of the different few-body techniques developed in nuclear physics and their applications to explore the structural properties of neutron-rich unstable nuclei, the so-called halo nuclei.

In the first three chapters, the authors discuss important aspects of wave optics on surfaces and at small scales, such as the optical interference near surfaces, the physical origin of the index of refraction, and how imaging optical fields can be used to enhance resolution in optical diffraction microscopy.

This is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation.

This book provides a pedagogical introduction to the rapidly growing field of reheating after inflation.

This primer describes the general model independent searches for new physics phenomena beyond the Standard Model of particle physics.

This book reviews various modified gravity models, including those with modifications in the pure gravitational sector; The book is unique in bringing together all the current alternatives to Einstein gravity in one source and serves as an excellent starting point for graduate students and other newcomers seeking an overview.

This book shares essential insights into the formation and properties of ionic interfaces based on the energy level structures of their interfaces obtained using a surface science approach.

This book presents a novel mathematical formalism, based on the tetrad formulation of differential geometry, for describing cosmological observables exactly and conveniently.

This book presents a new diagnostic approach that utilizes complex statistical, correlation, fractal, and singular analysis of spatial distribution of the Stokes vector of scattered polarized light in different diffraction zones.

This book introduces readers to state-of-the-art theoretical and simulation techniques for determining transport in complex band structure materials and nanostructured-geometry materials, linking the techniques developed by the electronic transport community to the materials science community.