Author : Fiorenzo Bastianelli
Publisher : Cambridge University Press
Page : 47 pages
File Size : 10,85 MB
Release : 2006-07-20
Category : Science
ISBN : 1139456849
This book introduces path integrals, a powerful method for describing quantum phenomena, and then uses them to compute anomalies in quantum field theories. An advanced text for researchers and graduate students of quantum field theory and string theory, it also provides a stand-alone introduction to path integrals in quantum mechanics.
Author : Kazuo Fujikawa
Publisher : Oxford University Press
Page : 297 pages
File Size : 13,42 MB
Release : 2004-04-29
Category : Mathematics
ISBN : 0198529139
The Feynman path integrals are becoming increasingly important in the applications of quantum mechanics and field theory. The path integral formulation of quantum anomalies, i.e. the quantum breaking of certain symmetries, can now cover all the known quantum anomalies in a coherent manner. In this book the authors provide an introduction to the path integral method in quantum field theory and its applications to the analyses of quantum anomalies. No previous knowledge of fieldtheory beyond the advanced undergraduate quantum mechanics is assumed. The book provides the first coherent introductory treatment of the path integral formulation of chiral and Weyl anomalies, with applications to gauge theory in two and four dimensions, conformal field theory and string theory. Explicitand elementary path integral calculations of most of the quantum anomalies covered are given. The conceptual basis of the path integral bosonization in two-dimensional theory, which may have applications to condensed matter theory, for example, is clarified. The book also covers the recent interesting developments in the treatment of fermions and chiral anomalies in lattice gauge theory.
Author : Belal E. Baaquie
Publisher : Cambridge University Press
Page : 437 pages
File Size : 18,41 MB
Release : 2014-03-27
Category : Science
ISBN : 1139867334
Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schrödinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.
Author : Pierre Cartier
Publisher : Cambridge University Press
Page : 7 pages
File Size : 22,4 MB
Release : 2006-11-30
Category : Science
ISBN : 1139462881
In this text, Cartier and DeWitt-Morette, using their complementary interests and expertise, successfully condense and apply the essentials of Functional Integration to a great variety of systems, showing this mathematically elusive technique to be a robust, user friendly and multipurpose tool.
Author : Stephen A. Fulling
Publisher : Cambridge University Press
Page : 332 pages
File Size : 41,53 MB
Release : 1989-08-24
Category : Mathematics
ISBN : 9780521377683
The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. This book provides, for mathematicians, an introduction to this field of physics in a language and from a viewpoint which such a reader should find congenial. Physicists should also gain from reading this book a sound grasp of various aspects of the theory, some of which have not been particularly emphasised in the existing review literature. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the 'Klein' paradox, particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalisation of the stress tensor. The style is pedagogic rather than formal; some knowledge of general relativity and differential geometry is assumed, but the author does supply background material on functional analysis and quantum field theory as required. The book arose from a course taught to graduate students and could be used for self-study or for advanced courses in relativity and quantum field theory.
Author : Lev V. Prokhorov
Publisher : Cambridge University Press
Page : 485 pages
File Size : 14,11 MB
Release : 2011-09-22
Category : Science
ISBN : 1139500902
The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.
Author : Bryce Seligman DeWitt
Publisher :
Page : 1053 pages
File Size : 23,86 MB
Release : 2003
Category : Quantum field theory
ISBN : 9780198712879
Author : Yitzhak Frishman
Publisher : Cambridge University Press
Page : 455 pages
File Size : 38,32 MB
Release : 2010-04-08
Category : Science
ISBN : 1139486489
Providing a new perspective on quantum field theory, this book is useful for graduate students and researchers within and outside the field. It describes non-perturbative methods, and explores two-dimensional and four-dimensional gauge dynamics using those methods. Applications are thoroughly described.
Author : Erick J. Weinberg
Publisher : Cambridge University Press
Page : 341 pages
File Size : 44,6 MB
Release : 2012-08-16
Category : Science
ISBN : 0521114632
An overview of classical solutions and their consequences in quantum field theory, high energy physics and cosmology for graduates and researchers.
Author : Daniel S. Freed
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 46,15 MB
Release : 2019-08-23
Category : Mathematics
ISBN : 1470452065
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
