## subcategories

**Field Theory** (18)

**Geometry & Physics** (18)

**Quaternions** (7)

**String Theory** (26)

## e-books in Mathematical Physics category

**Harmonic Oscillators and Two-by-two Matrices in Symmetry Problems in Physics**

by

**Young Suh Kim (ed.)**-

**MDPI AG**,

**2017**

With a degree of exaggeration, modern physics is the physics of harmonic oscillators and two-by-two matrices. Indeed, they constitute the basic language for the symmetry problems in physics, and thus the main theme of this journal.

(

**246**views)

**Lecture Notes on Mathematical Methods of Classical Physics**

by

**Vicente Cortes, Alexander S. Haupt**-

**arXiv**,

**2016**

Topics include Lagrangian Mechanics, Hamiltonian Mechanics, Hamilton-Jacobi Theory, Classical Field Theory formulated in the language of jet bundles, field theories such as sigma models, gauge theory, and Einstein's theory of general relativity.

(

**1915**views)

**Foundations Of Potential Theory**

by

**Oliver Dimon Kellog**-

**Springer**,

**1929**

The present volume gives a systematic treatment of potential functions. It has a purpose to serve as an introduction for students and to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications.

(

**505**views)

**Differential Equations of Mathematical Physics**

by

**Max Lein**-

**arXiv**,

**2015**

These lecture notes give an overview of how to view and solve differential equations that are common in physics. They cover Hamilton's equations, variations of the Schroedinger equation, the heat equation, the wave equation and Maxwell's equations.

(

**2752**views)

**Little Magnetic Book**

by

**Nicolas Raymond**-

**arXiv**,

**2014**

'Little Magnetic Book' is devoted to the spectral analysis of the magnetic Laplacian in various geometric situations. In particular the influence of the geometry on the discrete spectrum is analysed in many asymptotic regimes.

(

**1434**views)

**Introduction to Spectral Theory of SchrÃ¶dinger Operators**

by

**A. Pankov**-

**Vinnitsa State Pedagogical University**,

**2006**

Contents: Operators in Hilbert spaces; Spectral theorem of self-adjoint operators; Compact operators and the Hilbert-Schmidt theorem; Perturbation of discrete spectrum; Variational principles; One-dimensional Schroedinger operator; etc.

(

**4134**views)

**Quantum Spin Systems on Infinite Lattices**

by

**Pieter Naaijkens**-

**arXiv**,

**2013**

These are the lecture notes for a one semester course at Leibniz University Hannover. The main aim of the course is to give an introduction to the mathematical methods used in describing discrete quantum systems consisting of infinitely many sites.

(

**1944**views)

**Navier-Stokes Equations: On the Existence and the Search Method for Global Solutions**

by

**Solomon I. Khmelnik**-

**MiC**,

**2011**

In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional.

(

**4270**views)

**Funky Mathematical Physics Concepts**

by

**Eric L. Michelsen**-

**UCSD**,

**2012**

This text covers some of the unusual or challenging concepts in graduate mathematical physics. This work is meant to be used with any standard text, to help emphasize those things that are most confusing for new students.

(

**2557**views)

**Graph and Network Theory in Physics: A Short Introduction**

by

**Ernesto Estrada**-

**arXiv**,

**2013**

Text consisting of some of the main areas of research in graph theory applied to physics. It includes graphs in condensed matter theory, such as the tight-binding and the Hubbard model. It follows the study of graph theory and statistical physics...

(

**4176**views)

**Lectures on Integrable Hamiltonian Systems**

by

**G.Sardanashvily**-

**arXiv**,

**2013**

We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. This is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and systems with time-dependent parameters.

(

**3568**views)

**Euclidean Random Matrices and Their Applications in Physics**

by

**A. Goetschy, S.E. Skipetrov**-

**arXiv**,

**2013**

We review the state of the art of the theory of Euclidean random matrices, focusing on the density of their eigenvalues. Both Hermitian and non-Hermitian matrices are considered and links with simpler random matrix ensembles are established.

(

**2809**views)

**Mathematics for Theoretical Physics**

by

**Jean Claude Dutailly**-

**arXiv**,

**2012**

This is a comprehensive and precise coverage of the mathematical concepts and tools used in present theoretical physics: differential geometry, Lie groups, fiber bundles, Clifford algebra, differential operators, normed algebras, connections, etc.

(

**7573**views)

**Step-by-Step BS to PhD Math/Physics**

by

**Alex Alaniz**-

**UC Riverside**,

**2013**

These are step-by-verifiable-step notes which are designed to help students with a year of calculus based physics who are about to enroll in ordinary differential equations go all the way to doctoral foundations in either mathematics or physics.

(

**6457**views)

**Tensor Techniques in Physics: a concise introduction**

by

**Roy McWeeny**-

**Learning Development Institute**,

**2011**

Contents: Linear vector spaces; Elements of tensor algebra; The tensor calculus (Volume elements, tensor densities, and volume integrals); Applications in Relativity Theory (Elements of special relativity, Tensor form of Maxwell's equations).

(

**6768**views)

**Introduction to Mathematical Physics**

by

**Alex Madon**-

**Wikibooks**,

**2010**

The goal of this book is to propose an ensemble view of modern physics. The coherence between various fields of physics is insured by following two axes: a first is the universal mathematical language; the second is the study of the N body problem.

(

**3168**views)

**Lie Systems: Theory, Generalisations, and Applications**

by

**J.F. Carinena, J. de Lucas**-

**arXiv**,

**2011**

Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping.

(

**4029**views)

**Physics, Topology, Logic and Computation: A Rosetta Stone**

by

**John C. Baez, Mike Stay**-

**arXiv**,

**2009**

There is extensive network of analogies between physics, topology, logic and computation. In this paper we make these analogies precise using the concept of 'closed symmetric monoidal category'. We assume no prior knowledge of category theory.

(

**4762**views)

**Lectures on Three-Dimensional Elasticity**

by

**P. G. Ciarlet**-

**Tata Institute of Fundamental Research**,

**1983**

In this book a non-linear system of partial differential equations will be established as a mathematical model of elasticity. An energy functional will be established and existence results will be studied in the second chapter.

(

**4012**views)

**LieART: A Mathematica Application for Lie Algebras and Representation Theory**

by

**Robert Feger, Thomas W. Kephart**-

**arXiv**,

**2012**

We present the Mathematica application LieART (Lie Algebras and Representation Theory) for computations in Lie Algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations.

(

**4053**views)

**Lectures on Nonlinear Waves And Shocks**

by

**Cathleen S. Morawetz**-

**Tata Institute Of Fundamental Research**,

**1981**

Introduction to certain aspects of gas dynamics concentrating on some of the most important nonlinear problems, important not only from the engineering or computational point of view but also because they offer great mathematical challenges.

(

**3947**views)

**Lectures on Diffusion Problems and Partial Differential Equations**

by

**S.R.S. Varadhan**-

**Tata Institute of Fundamental Research**,

**1989**

Starting from Brownian Motion, the lectures quickly got into the areas of Stochastic Differential Equations and Diffusion Theory. The section on Martingales is based on additional lectures given by K. Ramamurthy of the Indian Institute of Science.

(

**4197**views)

**Topics in Spectral Theory**

by

**Vojkan Jaksic**-

**McGill University**,

**2005**

The subject of these lecture notes is spectral theory of self-adjoint operators and some of its applications to mathematical physics. The main theme is the interplay between spectral theory of self-adjoint operators and classical harmonic analysis.

(

**4069**views)

**Solitons**

by

**David Tong**-

**University of Cambridge**,

**2005**

These lectures cover aspects of solitons with focus on applications to the quantum dynamics of supersymmetric gauge theories and string theory. The lectures consist of four sections, each dealing with a different soliton.

(

**4088**views)

**Mathemathical Methods of Theoretical Physics**

by

**Karl Svozil**-

**Edition Funzl**,

**2012**

This book presents the course material for mathemathical methods of theoretical physics intended for an undergraduate audience. The author most humbly presents his own version of what is important for standard courses of contemporary physics.

(

**4268**views)

**Lectures on the Singularities of the Three-Body Problem**

by

**C.L. Siegel**-

**Tata Institute of Fundamental Research**,

**1967**

From the table of contents: The differential equations of mechanics; The three-body problem : simple collisions (The n-body problem); The three-body problem: general collision (Stability theory of solutions of differential equations).

(

**4272**views)

**A Set of Appendices on Mathematical Methods for Physics Students**

by

**Anne Fry, Amy Plofker, Sarah-marie Belcastro**,

**1996**

Useful mathematical background for physics students at all undergraduate levels. Topics: Matrices, Eigenvalues and Eigenvectors, Intro To Differential Equations, Integration, Fourier Analysis and Transforms, Converting Sums to Integrals, etc.

(

**4968**views)

**Theoretical Physics**

by

**W. Wilson**-

**Dutton**,

**1931**

The purpose of the present work is to present an account of the theoretical side of physics which, without being too elaborate, will be sufficiently comprehensive to be useful to teachers and students. This volume deals with mechanics and heat.

(

**4677**views)

**Mathematical Physics: Problems and Solutions**

by

**G. S. Beloglazov, et al.**-

**Samara University Press**,

**2010**

The present Proceedings is intended to be used by the students of physical and mechanical-mathematical departments of the universities, who are interested in acquiring a deeper knowledge of the methods of mathematical and theoretical physics.

(

**4852**views)

**A Window into Zeta and Modular Physics**

by

**Klaus Kirsten, Floyd L. Williams**-

**Cambridge University Press**,

**2010**

This book provides an introduction, with applications, to three interconnected mathematical topics: zeta functions in their rich variety; modular forms; vertex operator algebras. Applications of the material to physics are presented.

(

**4925**views)

**Mathematical Physics II**

by

**Boris Dubrovin**-

**SISSA**,

**2008**

These are lecture notes on various topics in analytic theory of differential equations: Singular points of solutions to analytic differential equations; Monodromy of linear differential operators with rational coefficients.

(

**9507**views)

**Lecture Notes on Quantum Brownian Motion**

by

**Laszlo Erdos**-

**arXiv**,

**2010**

Einstein's kinetic theory of the Brownian motion, based upon water molecules bombarding a heavy pollen, provided an explanation of diffusion from the Newtonian mechanics. It is a challenge to verify the diffusion from the Schroedinger equation.

(

**3958**views)

**Nonlinear Physics (Solitons, Chaos, Localization)**

by

**Nikos Theodorakopoulos**-

**Universitaet Konstanz**,

**2006**

This set of lectures describes some of the basic concepts mainly from the angle of condensed matter / statistical mechanics, an area which provided an impressive list of nonlinearly governed phenomena over the last fifty years.

(

**4590**views)

**Mathematics for Physics: A Guided Tour for Graduate Students**

by

**Michael Stone, Paul Goldbart**-

**Cambridge University Press**,

**2009**

This book provides a graduate-level introduction to the mathematics used in research in physics. It focuses on differential and integral equations, Fourier series, calculus of variations, differential geometry, topology and complex variables.

(

**11416**views)

**Special Functions and Their Symmetries: Postgraduate Course in Applied Analysis**

by

**Vadim Kuznetsov, Vladimir Kisil**-

**University of Leeds**,

**2003**

This text presents fundamentals of special functions theory and its applications in partial differential equations of mathematical physics. The course covers topics in harmonic, classical and functional analysis, and combinatorics.

(

**8647**views)

**Interactions, Strings and Isotopies in Higher Order Anisotropic Superspaces**

by

**Sergiu I. Vacaru**-

**arXiv**,

**2001**

The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions. The main subjects are in the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces.

(

**6038**views)

**Floer Homology, Gauge Theory, and Low Dimensional Topology**

by

**David Ellwood, at al.**-

**American Mathematical Society**,

**2006**

Mathematical gauge theory studies connections on principal bundles. The book provides an introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds.

(

**6779**views)

**Random Matrices**

by

**B. Eynard**,

**2001**

This is an introductory course about random matrices. These notes will give the reader a smell of that fascinating tool for physicists and mathematicians that are Random Matrices, and they can give the envy to learn and search more.

(

**5152**views)

**Mirror Symmetry**

by

**Cumrun Vafa, Eric Zaslow**-

**American Mathematical Society**,

**2003**

The book provides an introduction to the field of mirror symmetry from both a mathematical and physical perspective. After covering the relevant background material, the monograph is devoted to the proof of mirror symmetry from various viewpoints.

(

**6395**views)

**Invariance Theory, the Heat Equation and the Atiyah-Singer Index Theorem**

by

**Peter B. Gilkey**-

**Publish or Perish Inc.**,

**1984**

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas and the Gauss-Bonnet theorem.

(

**4743**views)

**A Mathematics Primer for Physics Graduate Students**

by

**Andrew E. Blechman**,

**2007**

The author summarizes most of the more advanced mathematical trickery seen in electrodynamics and quantum mechanics in simple and friendly terms with examples. Mathematical tools such as tensors or differential forms are covered in this text.

(

**15837**views)

**An Introduction to Hyperbolic Analysis**

by

**Andrei Khrennikov, Gavriel Segre**-

**arXiv**,

**2005**

Contents: The hyperbolic algebra as a bidimensional Clifford algebra; Limits and series in the hyperbolic plane; The hyperbolic Euler formula; Analytic functions in the hyperbolic plane; Multivalued functions on the hyperbolic plane; etc.

(

**6788**views)

**An Introduction to Topos Physics**

by

**Marios Tsatsos**-

**arXiv**,

**2008**

The basic notion of how topoi can be utilized in physics is presented here. Topos and category theory serve as valuable tools which extend our ordinary set-theoretical conceptions, can give rise to new descriptions of quantum physics.

(

**4763**views)

**Introduction to Quantum Integrability**

by

**A. Doikou, S. Evangelisti, G. Feverati, N. Karaiskos**-

**arXiv**,

**2010**

The authors review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. A short review on quantum groups as well as the quantum inverse scattering method is also presented.

(

**4532**views)

**Feynman Diagrams and Differential Equations**

by

**Mario Argeri, Pierpaolo Mastrolia**-

**arXiv**,

**2007**

The authors review the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the technique, we discuss its application in the context of corrections to the photon propagator in QED.

(

**7234**views)

**Classical and Quantum Mechanics via Lie algebras**

by

**Arnold Neumaier, Dennis Westra**-

**arXiv**,

**2011**

This book presents classical, quantum, and statistical mechanics in an algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups.

(

**7471**views)

**Neutrosophic Physics: More Problems, More Solutions**

by

**F. Smarandache**-

**North-European Scientific Publishers**,

**2010**

Neutrosophic logics is one of the promising research instruments, which could be successfully applied by a theoretical physicist. Neutrosophic logics states that neutralities may be between any physical states, or states of space-time.

(

**4773**views)

**Clifford Algebra, Geometric Algebra, and Applications**

by

**Douglas Lundholm, Lars Svensson**-

**arXiv**,

**2009**

These are lecture notes for a course on the theory of Clifford algebras. The various applications include vector space and projective geometry, orthogonal maps and spinors, normed division algebras, as well as simplicial complexes and graph theory.

(

**7431**views)

**The Landscape of Theoretical Physics**

by

**Matej Pavsic**-

**arXiv**,

**2006**

This a book is for those who would like to learn something about special and general relativity beyond the usual textbooks, about quantum field theory, the elegant Fock-Schwinger-Stueckelberg proper time formalism, and much more.

(

**7484**views)

**An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics**

by

**William Elwood Byerly**-

**Ginn and company**,

**1893**

From the table of contents: Development in Trigonometric Series; Convergence of Fourier's Series; Solution of Problems in Physics by the Aid of Fourier's Integrals and Fourier's Series; Zonal Harmonics; Spherical Harmonics; Cylindrical Harmonics; ...

(

**9681**views)

**Random Matrix Models and Their Applications**

by

**Pavel Bleher, Alexander Its**-

**Cambridge University Press**,

**2001**

The book covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.

(

**9734**views)

**Group Theory**

by

**Ferdi Aryasetiawan**-

**University of Lund**,

**1997**

The text deals with basic Group Theory and its applications. Contents: Abstract Group Theory; Theory of Group Representations; Group Theory in Quantum Mechanics; Lie Groups; Atomic Physics; The Group SU2: Isospin; The Point Groups; The Group SU3.

(

**8114**views)

**Lie Theory and Special Functions**

by

**Willard Miller**-

**Academic Press**,

**1968**

The book studies the role played by special function theory in the formalism of mathematical physics. It demonstrates that special functions which arise in mathematical models are dictated by symmetry groups admitted by the models.

(

**7287**views)

**Lie Groups in Physics**

by

**G. 't Hooft, M. J. G. Veltman**-

**Utrecht University**,

**2007**

Contents: Quantum mechanics and rotation invariance; The group of rotations in three dimensions; More about representations; Ladder operators; The group SU(2); Spin and angular distributions; Isospin; The Hydrogen Atom; The group SU(3); etc.

(

**8314**views)

**Partial Differential Equations of Mathematical Physics**

by

**William W. Symes**-

**Rice University**,

**2006**

This course aims to make students aware of the physical origins of the main partial differential equations of classical mathematical physics, including the equations of fluid and solid mechanics, thermodynamics, and classical electrodynamics.

(

**8697**views)

**The Octonions**

by

**John C. Baez**-

**University of California**,

**2001**

The octonions are the largest of the four normed division algebras. The author describes them and their relation to Clifford algebras and spinors, Bott periodicity, projective and Lorentzian geometry, Jordan algebras, and the exceptional Lie groups.

(

**12210**views)

**Introduction to Physics for Mathematicians**

by

**Igor Dolgachev**,

**1996**

A set of class notes taken by math graduate students, the goal of the course was to introduce some basic concepts from theoretical physics which play so fundamental role in a recent intermarriage between physics and pure mathematics.

(

**9468**views)

**Applications of global analysis in mathematical physics**

by

**Jerrold E. Marsden**-

**Publish or Perish, inc**,

**1974**

The book introduces some methods of global analysis which are useful in various problems of mathematical physics. The author wants to make use of ideas from geometry to shed light on problems in analysis which arise in mathematical physics.

(

**10003**views)

**Elements for Physics: Quantities, Qualities, and Intrinsic Theories**

by

**Albert Tarantola**-

**Springer**,

**2006**

Reviews Lie groups, differential geometry, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. The theory of heat conduction and the theory of linear elastic media are studied in detail.

(

**10092**views)

**Mathematics for the Physical Sciences**

by

**Herbert S Wilf**-

**Dover Publications**,

**1962**

The book for the advanced undergraduates and graduates in the natural sciences. Vector spaces and matrices, orthogonal functions, polynomial equations, asymptotic expansions, ordinary differential equations, conformal mapping, and extremum problems.

(

**20621**views)