Series: Universitext
1st ed. 2017, XII, 613 p. 40 illus.
Softcover
ISBN 978-3-319-68438-3
* Explains the Standard Model to students of both mathematics and
physics
* Covers both the specific gauge theory of the Standard Model and
generalizations
* Highly accessible and self-contained
The Standard Model is the foundation of modern particle and high energy physics. This
book explains the mathematical background behind the Standard Model, translating
ideas from physics into a mathematical language and vice versa.
The first part of the book covers the mathematical theory of Lie groups and Lie algebras,
fibre bundles, connections, curvature and spinors. The second part then gives a detailed
exposition of how these concepts are applied in physics, concerning topics such as the
Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs
boson and mass generation of gauge bosons and fermions. The book also contains a
chapter on advanced and modern topics in particle physics, such as neutrino masses, CP
violation and Grand Unification.
This carefully written textbook is aimed at graduate students of mathematics and physics.
It contains numerous examples and more than 150 exercises, making it suitable for
self-study and use alongside lecture courses. Only a basic knowledge of differentiable
manifolds and special relativity is required, summarized in the appendix.
Series: Springer INdAM Series, Vol. 23
1st ed. 2017, X, 269 p. 12 illus., 11 illus. in color.
Hardcover
ISBN 978-3-319-67518-3
* Offers ultimative research articles on cutting-edge topics
* Written leading international experts
* Provides an overview of the state of the art in a wide spectrum of
active research lines
The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic
geometry” held in Rome in November 2015. It offers a panoramic view of a selection of
cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and
octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal
geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5*
8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable
systems. The workshop was held in honor of Simon Salamon, a leading international
scholar at the forefront of academic research who has made significant contributions
to all these subjects. The articles published here represent a compelling testimony to
Salamon’s profound and longstanding impact on the mathematical community. Target
readership includes graduate students and researchers working in Riemannian and
complex geometry, Lie theory and mathematical physics.
Series: Probability Theory and Stochastic Modelling, Vol. 83-84
1st ed. 2018, LIII, 1371 p. 2 volume-set.
Hardcover
ISBN 978-3-319-59820-8
* First comprehensive presentation of state of the art theory of
mean field games with special emphasis on the probabilistic
approachNumerous applications with explicit examples including
numerical solutions
* Self-contained treatment of related topics such as analysis on
Wasserstein space and mean field control problems
This two-volume set offers an expansive overview of the probabilistic approach to game
models and their applications. Considered the first comprehensive treatment of the
theory of mean field games, much of the content is original and has been designed
especially for the purpose of this book. Volume I of the set is entirely devoted to the
theory of mean field games without a common noise, whereas Volume II analyzes mean
field games in which the players are subject to games with a common noise.
Together, both Volume I and Volume II will benefit researchers in the field as well as
PhD and graduate students working on the subject due to the self-contained nature and
applications with explicit examples throughout.
625pp Dec 2017
ISBN: 978-981-3226-43-2
This textbook gives an introduction to Partial Differential Equations (PDEs), for any reader wishing to learn and understand the basic concepts, theory, and solution techniques of elementary PDEs. The only prerequisite is an undergraduate course in Ordinary Differential Equations. This work contains a comprehensive treatment of the standard second-order linear PDEs, the heat equation, wave equation, and Laplace's equation. First-order and some common nonlinear PDEs arising in the physical and life sciences and their solutions are also covered.
This textbook also includes an introduction to Fourier series and their properties, an introduction to regular Sturm*Liouville boundary value problems, special functions of mathematical physics, a treatment of nonhomogeneous equations and boundary conditions using methods such as Duhamel's principle, and an introduction to the finite difference technique for the numerical approximation of solutions. All results have been rigorously justified or precise references to justifications in more advanced sources have been cited. Appendices providing a background in complex analysis and linear algebra are also included for readers with limited prior exposure to those subjects.
The textbook also includes material from which instructors could create a one- or two-semester course in PDEs. Students may also study this material in preparation for a graduate school (masters or doctoral) course in PDEs.
Introduction
First-Order Partial Differential Equations
Fourier Series
The Heat Equation
The Wave Equation
The Laplace Equation
Sturm*Liouville Theory
Special Functions
Applications of PDEs in the Physical Sciences
Nonhomogeneous Initial Boundary Value Problems
Nonlinear Partial Differential Equations
Numerical Solutions to PDEs Using Finite Differences
Appendices:
Readership: Mathematics, physical and life sciences, and engineering undergraduate students interested in partial differential equations.