This collection of invited lectures (at the Conference on Secondary Calculus and Cohomological Physics, Moscow) reflects the state-of-the-art in a new branch of mathematics and mathematical physics arising at the intersection of geometry of nonlinear differential equations, quantum field theory, and cohomological algebra. This is the first comprehensive and self-contained book on modern quantum field theory in the context of cohomological methods and the geometry of nonlinear PDEs. It features: an up-to-date and self-contained exposition of the newest results in cohomological aspects of quantum field theory and the geometry of PDEs; a new look at interrelations among cohomology theory, the geometry of PDEs, and field theory; and, application to Batalin-Vilkovisky formalism, BRST formalism, anomalies, and quantum dynamics.
This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations.
This book is dedicated to fundamentals of a new theory, which is an analog of affine algebraic geometry for (nonlinear) partial differential equations.
This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields. This EMS volume consists of two parts.
This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals.
In the 1970's there was considerable development of a line of ideas pioneered by D. Sullivan (Su?0) and D. Quillen [Q69]. The main idea, introduced by Serre |Seá3], was that of localization, at a prime p, ...
This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry.
Practical text focuses on fundamental applied math needed to deal with physics and engineering problems: elementary vector calculus, special functions of mathematical physics, calculus of variations, much more. 1968 edition.
The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere.
This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics.
This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily ...