Author : Fumio Hiroshima
Publisher : Walter de Gruyter GmbH & Co KG
Page : 558 pages
File Size : 42,50 MB
Release : 2020-03-09
Category : Mathematics
ISBN : 3110403544
This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. In the second volume, these ideas are applied principally to a rigorous treatment of some fundamental models of quantum field theory.
Author : József Lörinczi
Publisher : Walter de Gruyter
Page : 521 pages
File Size : 47,85 MB
Release : 2011-08-29
Category : Mathematics
ISBN : 3110203731
This monograph offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. These ideas are then applied principally to a rigorous treatment of some fundamental models of quantum field theory. In this self-contained presentation of the material both beginners and experts are addressed, while putting emphasis on the interdisciplinary character of the subject.
Author : Anne Boutet de Monvel
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 45,16 MB
Release : 2006-12-15
Category : Science
ISBN : 3764374349
Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous contributions; this book arose from an international symposium held in honour of Bros on the occasion of his 70th birthday. Key topics in this volume include: Analytic structures of Quantum Field Theory (QFT), renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime.
Author : Romeo Brunetti
Publisher : Springer
Page : 460 pages
File Size : 30,64 MB
Release : 2015-09-04
Category : Science
ISBN : 3319213539
This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.
Author : Kasia Rejzner
Publisher : Springer
Page : 186 pages
File Size : 32,68 MB
Release : 2016-03-16
Category : Science
ISBN : 3319259016
Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.
Author : Thomas-Paul Hack
Publisher : Springer
Page : 129 pages
File Size : 20,45 MB
Release : 2015-08-17
Category : Science
ISBN : 3319218948
This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.>
Author : Ivan Nyklíček
Publisher : Springer
Page : 246 pages
File Size : 16,74 MB
Release : 2008-11-01
Category : Psychology
ISBN : 9780387510583
An increasing number of studies have been conducted on the role of expression and regulation of emotion in health. Emotion Regulation addresses the question of these studies from diverse angles while encompassing conceptual, developmental, and clinical issues. Central concepts discussed in this volume that are related to health include: coping styles and aggression, alexithymia, emotional intelligence, emotional expression and depression, emotional expression and anxiety disorders, in addition to the emotional competence in children. The book is unique in describing up-to-date theories and empirical research in the area of emotional expression and health.
Author : Robin Ticciati
Publisher : Cambridge University Press
Page : 720 pages
File Size : 36,47 MB
Release : 1999-06-13
Category : Mathematics
ISBN : 052163265X
This should be a useful reference for anybody with an interest in quantum theory.
Author : Stephen A. Fulling
Publisher : Cambridge University Press
Page : 332 pages
File Size : 14,81 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 : G. B. Folland
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 35,41 MB
Release : 2008-08-26
Category : Mathematics
ISBN : 0821847058
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam-Weinberg model of electromagnetic and weak interactions.
