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436 results in Theoretical Physics and Mathematical Physics

Page 1 of 22

Celestial Mechanics
  • Classical and Modern Methods
  • Antonio Giorgilli, Ugo Locatelli, Marco Sansottera
  • Coming soon
  • Expected online publication date:
    May 2026
    Print publication:
    31 May 2026
  • Starting from ancient astronomy, this text follows the development of celestial mechanics culminating in applications of the most recent results concerning stability of planetary orbits: Kolmogorov's and Nekhoroshev's theorems. Key topics covered include: a historical introduction from ancient astronomy to Kepler and Newton; Lagrange's perturbation theory; the problem of three bodies, with a discussion of Levi-Civita regularization and of Sundman's theorem; methods of algebraic calculation of perturbation series, including a discussion of non-convergence due to the accumulation of small divisors; and a complete application of Kolmogorov's and Nekhoroshev's theorems. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students, and for young researchers. Its approach allows students to learn about perturbation methods leading to advanced results.

Half a Century of Supergravity
  • Bridging between Einstein and the Quantum
  • Edited by Anna Ceresole, Gianguido Dall'Agata
  • Coming soon
  • Expected online publication date:
    May 2026
    Print publication:
    31 May 2026
  • This volume gathers the contributions of founders, experts and practitioners of supergravity celebrating the 50th anniversary of its birth, discussing the history of the field and its modern applications to high energy physics, mathematics, particle physics and cosmology. Since its discovery in the mid-1970s, fully understanding its symmetries and structures, the physical implications, permitted generalizations and the connections with other theories have been highly nontrivial challenges. Whether supergravity will be proven true by experiments or it remains a mathematical framework, the theory is elegant, intriguing, rich and entertaining. Many agree that it will continue to be an inspiration and theoretical laboratory for quantum gravity, as well as an intellectual achievement that expresses the highest levels of human creativity in our effort to understand the cosmos and its rules. Current and future practitioners, and historians of science, will value both the comprehensive history and future perspectives of the field within.

Quantum Physics
  • Fundamentals and Applications
  • Olivier Pujol, Robert Carles
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    28 February 2026
  • An impressively comprehensive textbook adopting a phenomenological approach to quantum physics. The chapters cover everything from basic definitions of key concepts to detailed discussions of the underlying theoretical framework, walking students step-by-step through the necessary mathematics and drawing clear connections between the theory and the most important modern research applications including quantum optics, fluids, nanophysics, entanglement, information, and relativity. With this book, students and researchers will have access to hundreds of real-world examples, exercises, and illustrations to support and expand their understanding. Instructors can tailor the content to suit the length and level of their course and will have access to an online solutions manual with fully worked solutions to all 300+ exercises in the book. Other online resources include Python simulations, additional exercises, and detailed appendices.

Bethe Ansatz
  • Gleb Arutyunov
  • Coming soon
  • Expected online publication date:
    April 2026
    Print publication:
    30 April 2026
  • The Bethe Ansatz is a powerful method in the theory of quantum integrable models, essential for determining the energy spectrum of dynamical systems - from spin chains in magnetism to models in high-energy physics. This book provides a comprehensive introduction to the Bethe ansatz, from its historical roots to modern developments. First introduced by Hans Bethe in 1931, the method has evolved into a universal framework encompassing algebraic, analytic, thermodynamic, and functional forms. The book explores various Bethe ansatz techniques and their interrelations, covering both coordinate and algebraic versions, with particular attention to nested structures and functional relations involving transfer matrices. Advanced tools such as the separation of variables method are presented in detail. With a wealth of worked examples and precise calculations, this volume serves as an accessible and rigorous reference for graduate students and researchers in mathematical physics and integrable systems.

Tensors

Classical Mechanics
  • Subir Sarkar
  • Coming soon
  • Expected online publication date:
    March 2026
    Print publication:
    01 May 2027

Many-Body Green's Functions for Time-Dependent Problems
  • Giancarlo Calvanese Strinati
  • Coming soon
  • Expected online publication date:
    March 2026
    Print publication:
    31 March 2026
  • Quantum many-body systems are a central feature of condensed matter physics, relevant to important, modern research areas such as ultrafast light-matter interactions and quantum information. This book offers detailed coverage of the contour Green's function formalism – an approach that can be successfully applied to solve the quantum many-body and time-dependent problems present within such systems. Divided into three parts, the text provides a structured overview of the relevant theoretical and practical tools, with specific focus on the Schwinger-Keldysh formalism. Part I introduces the mathematical frameworks that make use of Green's functions in normal phase states. Part II covers fermionic superfluid phases with discussion of topics such as the BCS-BEC crossover and superconducting systems. Part III deals with the application of the Schwinger-Keldysh formalism to various topics of experimental interest. Graduate students and researchers will benefit from the book's comprehensive treatment of the subject matter and its novel arrangement of topics.

Gravitation for Theorists
  • Piljin Yi
  • Coming soon
  • Expected online publication date:
    February 2026
    Print publication:
    28 February 2026
  • Intended for graduate and advanced undergraduate students, this textbook is a thoroughly modern introduction to and a self-contained treatise on the theoretical and mathematical fundamentals of General Relativity. The chapters are organized into three parts, with the first covering Maxwell's theory of electromagnetism, the relativistic Kepler problem, and the systematics of the underlying geometry, with the more abstract notion of the fibre bundle relegated to the Appendix. The second part begins with a derivation of the Einstein equations and leads to topics such as cosmology, black holes, causal structures, and action principles. The third part covers the canonical formulation of field theory in general and General Relativity in particular, leading to the concept of the total energy in General Relativity and quantum phenomena with event horizons. The book minimizes historical references, focuses on modern tools, examples, and applications, and emphasizes the commonalities between relativistic gravity and gauge theory.

Quantum Cosmology
  • An Introduction
  • Jean-Luc Lehners
  • Coming soon
  • Expected online publication date:
    January 2026
    Print publication:
    28 February 2026
  • 'Quantum Cosmology' offers a guided introduction to the quantum aspects of the cosmos. Starting with an overview of early universe cosmology, the book builds up to advanced topics such as the Wheeler–DeWitt equation, gravitational path integrals, and the no-boundary proposal for the wave function of the universe. Readers will explore tunneling processes via Coleman–DeLuccia instantons, the quantum origin of primordial fluctuations, the thermodynamics of horizons, and basic notions of string cosmology. Concepts such as wormholes and semi-classical geometry are introduced with clarity and physical motivation. The book assumes some familiarity with general relativity and quantum mechanics, but little prior knowledge of cosmology. It includes a wide range of exercises, with solutions provided. Written in a pedagogical style, it bridges the gap between undergraduate courses and the research level in this frontier area of theoretical physics.

The Standard Model
  • A Practical Step-by-Step Guide
  • Marco Fabbrichesi
  • Coming soon
  • Expected online publication date:
    January 2026
    Print publication:
    23 October 2025
  • This innovative textbook has been designed with approachability and engagement at its forefront, using language reminiscent of a live lecture and interspersing the main text with useful advice and expansions. Striking a balance between theoretical- and experimental-led approaches, this book immediately immerses the reader in charge and neutral currents, which are at the core of the Standard Model, before presenting the gauge field, allowing the introduction of Feynman diagram calculations at an early stage. This novel and effective approach gives readers a head start in understanding the Model's predictions, stoking interest early on. With in-chapter problem sessions which help readers to build their mastery of the subject, clarifying notes on equations, end of chapter exercises to consolidate learning, and marginal comments to guide readers through the complexities of the Standard Model, this is the ideal book for graduate students studying high energy physics.

Full Quantum Effects in Condensed Matter Physics
  • Beyond the Born-Oppenheimer Approximation
  • Enge Wang
  • Coming soon
  • Expected online publication date:
    January 2026
    Print publication:
    31 January 2026
  • As physical science advances, theoretical simulations become increasingly reflective of realistic systems, and experimental observations become more precise and refined. Thus, going beyond the Born–Oppenheimer approximation is inevitable. This book bases its discussion of condensed matter physics on the Schrödinger equation, considering both nuclear and electronic degrees of freedom. Particular attention is given to two types of phenomena: those, such as nuclear quantum effects, for which the Born–Oppenheimer approximation, although applicable in principle, is progressively weakened in practice, and those that cannot be applied at all, such as phenomena exhibiting non-adiabatic effects. In practical systems, the full quantum nature of condensed matter, as emphasized in this book, cannot be overlooked when performing accurate simulations or measurements of material properties. This book offers state-of-the-art quantum theoretical and experimental methods, valuable for undergraduates, graduates, researchers, and industry professionals in fields such as physics, chemistry, materials science, energy, and environmental science.

Phase Transitions in the Theory of Lattice Gases
  • Barry Simon
  • Coming soon
  • Expected online publication date:
    November 2025
    Print publication:
    13 November 2025
  • The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that. Topics covered include correlation inequalities, Lee-Yang theorems, the Peierls method, the Hohenberg-Mermin-Wagner method, infrared bounds, random cluster methods, random current methods and BKT transition. The final section outlines major open problems to inspire future work. This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

Causal Fermion Systems
  • An Introduction to Fundamental Structures, Methods and Applications
  • Felix Finster, Sebastian Kindermann, Jan‐Hendrik Treude
  • Published online:
    15 November 2025
    Print publication:
    23 October 2025
  • The theory of causal fermion systems represents a novel approach to fundamental physics and is a promising candidate for a unified physical theory. This book offers a comprehensive overview of the theory, structured in four parts: the first lays the necessary mathematical and physical foundations; the second offers an introduction to the theory and the causal action principle; the third describes the mathematical tools for analyzing causal fermion systems; and the fourth gives an outlook on the key physical applications. With relevance across mathematical and theoretical physics, the book is aimed at graduate students and researchers interested in novel approaches to the structure of spacetime and alternative perspectives to the more established quantum field theories. It can be used for advanced courses in the subject or as a reference for research and self-guided study. Exercises are included at the end of each chapter to build and develop key concepts.

Quantum Mechanics
  • Lectures on Theoretical Physics
  • Volume 3
  • David Tong
  • Published online:
    27 June 2025
    Print publication:
    19 June 2025
  • The universe we live in is both strange and interesting. This strangeness comes about because, at the most fundamental level, the universe is governed by the laws of quantum mechanics. This is the most spectacularly accurate and powerful theory ever devised, one that has given us insights into many aspects of the world, from the structure of matter to the meaning of information. This textbook provides a comprehensive account of all things quantum. It starts by introducing the wavefunction and its interpretation as an ephemeral wave of complex probability, before delving into the mathematical formalism of quantum mechanics and exploring its diverse applications, from atomic physics and scattering, to quantum computing. Designed to be accessible, this volume is suitable for both students and researchers, beginning with the basics before progressing to more advanced topics.

Electromagnetism
  • Lectures on Theoretical Physics
  • Volume 2
  • David Tong
  • Published online:
    26 June 2025
    Print publication:
    19 June 2025
  • There are four forces in our universe. Two act only at the very smallest scales and one only at the very biggest. For everything inbetween, there is electromagnetism. The theory of electromagnetism is described by four gloriously simple and beautiful vector calculus equations known as the Maxwell equations. These are the first genuinely fundamental equations that we meet in our physics education and they survive, essentially unchanged, in our best modern theories of physics. They also serve as a blueprint for what subsequent laws of physics look like. This textbook takes us on a tour of the Maxwell equations and their many solutions. It starts with the basics of electric and magnetic phenomena and explains how their unification results in waves that we call light. It then describes more advanced topics such as superconductors, monopoles, radiation, and electromagnetism in matter. The book concludes with a detailed review of the mathematics of vector calculus.

Classical Mechanics
  • Lectures on Theoretical Physics
  • Volume 1
  • David Tong
  • Published online:
    26 June 2025
    Print publication:
    19 June 2025
  • Any education in theoretical physics begins with the laws of classical mechanics. The basics of the subject were laid down long ago by Galileo and Newton and are enshrined in the famous equation F=ma that we all learn in school. But there is much more to the subject and, in the intervening centuries, the laws of classical mechanics were reformulated to emphasis deeper concepts such as energy, symmetry, and action. This textbook describes these different approaches to classical mechanics, starting with Newton's laws before turning to subsequent developments such as the Lagrangian and Hamiltonian approaches. The book emphasises Noether's profound insights into symmetries and conservation laws, as well as Einstein's vision of spacetime, encapsulated in the theory of special relativity. Classical mechanics is not the last word on theoretical physics. But it is the foundation for all that follows. The purpose of this book is to provide this foundation.

Fluid Mechanics
  • Lectures on Theoretical Physics
  • Volume 4
  • David Tong
  • Published online:
    26 June 2025
    Print publication:
    19 June 2025
  • Take anything in the universe, put it in a box, and heat it up. Regardless of what you start with, the motion of the substance will be described by the equations of fluid mechanics. This remarkable universality is the reason why fluid mechanics is important. The key equation of fluid mechanics is the Navier-Stokes equation. This textbook starts with the basics of fluid flows, building to the Navier-Stokes equation while explaining the physics behind the various terms and exploring the astonishingly rich landscape of solutions. The book then progresses to more advanced topics, including waves, fluid instabilities, and turbulence, before concluding by turning inwards and describing the atomic constituents of fluids. It introduces ideas of kinetic theory, including the Boltzmann equation, to explain why the collective motion of 1023 atoms is, under the right circumstances, always governed by the laws of fluid mechanics.

General Relativity
  • A Graduate Course
  • Horatiu Nastase
  • Published online:
    24 April 2025
    Print publication:
    08 May 2025
  • This text on general relativity and its modern applications is suitable for an intensive one-semester course on general relativity, at the level of a Ph.D. student in physics. Assuming knowledge of classical mechanics and electromagnetism at an advanced undergraduate level, basic concepts are introduced quickly, with greater emphasis on their applications. Standard topics are covered, such as the Schwarzschild solution, classical tests of general relativity, gravitational waves, ADM parametrization, relativistic stars and cosmology, as well as more advanced standard topics like vielbein-spin connection formulation, trapped surfaces, the Raychaudhuri equation, energy conditions, the Petrov and Bianchi classifications and gravitational instantons. More modern topics, including black hole thermodynamics, gravitational entropy, effective field theory for gravity, the PPN expansion, the double copy and fluid-gravity correspondence, are also introduced using the language understood by physicists, without too abstract mathematics, proven theorems, or the language of pure mathematics.

Lectures on Mathematical Relativity
  • Justin Corvino, Pengzi Miao
  • Published online:
    03 April 2025
    Print publication:
    10 April 2025
  • This book introduces and explores some of the deep connections between Einstein's theory of gravitation and differential geometry. As an outgrowth of graduate summer schools, the presentation is aimed at graduate students in mathematics and mathematical physics, starting from the foundations of special and general relativity, and moving to more advanced results in geometric analysis and the Einstein constraint equations. Topics include the formulation of the Einstein field equation and the Einstein constraint equations; gluing construction of initial data sets which are Schwarzschild near infinity; and an introduction to the Riemannian Penrose inequality. While the book assumes a background in differential geometry and real analysis, a number of basic results in geometry are provided. There are well over 100 exercises, many woven into the fabric of the chapters as well as others collected at the end of chapters, to give readers a chance to engage and extend the text.

Uncovering Quantum Field Theory and the Standard Model
  • From Fundamental Concepts to Dynamical Mechanisms
  • Wolfgang Bietenholz, Uwe-Jens Wiese
  • Published online:
    06 February 2025
    Print publication:
    02 January 2025
  • This textbook provides an accessible introduction to quantum field theory and the Standard Model of particle physics. It adopts a distinctive pedagogical approach with clear, intuitive explanations to complement the mathematical exposition. The book begins with basic principles of quantum field theory, relating them to quantum mechanics, classical field theory, and statistical mechanics, before building towards a detailed description of the Standard Model. Its concepts and components are introduced step by step, and their dynamical roles and interactions are gradually established. Advanced topics of current research are woven into the discussion and key chapters address physics beyond the Standard Model, covering subjects such as axions, technicolor, and Grand Unified Theories. This book is ideal for graduate courses and as a reference and inspiration for experienced researchers. Additional material is provided in appendices, while numerous end-of-chapter problems and quick questions reinforce the understanding and prepare students for their own research.

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