› › Gauge Field Theory In Natural Geometric Language

Gauge Field Theory in Natural Geometric Language

Author : Daniel Canarutto

Publisher : Oxford University Press

Page : 330 pages

File Size : 41,64 MB

Release : 2020-10-06

Category : Mathematics

ISBN : 0192606212

Get eBook

Book Description

Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.



Gauge Field Theory in Natural Geometric Language

Author : Daniel Canarutto

Publisher : Oxford University Press, USA

Page : 362 pages

File Size : 32,28 MB

Release : 2020-10-05

Category : Mathematics

ISBN : 0198861494

Get eBook

Book Description

Gauge Field theory in Natural Geometric Language addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a brief, integrated approach that exploits standard and non-standard notions, as well as recent advances, in a natural geometric language in which the role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. In proposing an original bridge between physics and mathematics, this text will appeal not only to mathematicians who wish to understand some of the basic ideas involved in quantum particle physics, but also to physicists who are not satisfied with the usual mathematical presentations of their field.



An Introduction to Covariant Quantum Mechanics

Author : Josef Janyška

Publisher : Springer Nature

Page : 831 pages

File Size : 46,46 MB

Release : 2022-04-06

Category : Science

ISBN : 3030895890

Get eBook

Book Description

This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.



Natural and Gauge Natural Formalism for Classical Field Theorie

Author : L. Fatibene

Publisher : Springer Science & Business Media

Page : 374 pages

File Size : 49,62 MB

Release : 2013-06-29

Category : Science

ISBN : 9401723842

Get eBook

Book Description

In this book the authors develop and work out applications to gravity and gauge theories and their interactions with generic matter fields, including spinors in full detail. Spinor fields in particular appear to be the prototypes of truly gauge-natural objects, which are not purely gauge nor purely natural, so that they are a paradigmatic example of the intriguing relations between gauge natural geometry and physical phenomenology. In particular, the gauge natural framework for spinors is developed in this book in full detail, and it is shown to be fundamentally related to the interaction between fermions and dynamical tetrad gravity.



Recent Advances in Diffeologies and Their Applications

Author : Jean-Pierre Magnot

Publisher : American Mathematical Society

Page : 272 pages

File Size : 33,67 MB

Release : 2024-02-02

Category : Mathematics

ISBN : 1470472546

Get eBook

Book Description

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.



An Elementary Primer for Gauge Theory

Author : K. Moriyasu

Publisher : World Scientific

Page : 204 pages

File Size : 47,18 MB

Release : 1983

Category : Technology & Engineering

ISBN : 9789971950835

Get eBook

Book Description

Gauge theory is now recognized as one of the most revolutionary discoveries in physics since the development of quantum mechanics. This primer explains how and why gauge theory has dramatically changed our view of the fundamental forces of nature. The text is designed for the non-specialist. A new, intuitive approach is used to make the ideas of gauge theory accessible to both scientists and students with only a background in quantum mechanics. Emphasis is placed on the physics rather than the formalism.



The Diverse World of PDEs

Author : I. S. Krasil′shchik

Publisher : American Mathematical Society

Page : 236 pages

File Size : 24,49 MB

Release : 2023-08-23

Category : Mathematics

ISBN : 1470473550

Get eBook

Book Description

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.



Advanced Classical Field Theory

Author : G. Giachetta

Publisher : World Scientific

Page : 393 pages

File Size : 12,63 MB

Release : 2009

Category : Science

ISBN : 9812838961

Get eBook

Book Description

Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo are presented in a complete way. This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.



Structural Aspects Of Quantum Field Theory And Noncommutative Geometry (Second Edition) (In 2 Volumes)

Author : Gerhard Grensing

Publisher : World Scientific

Page : 1656 pages

File Size : 49,92 MB

Release : 2021-07-15

Category : Science

ISBN : 9811237093

Get eBook

Book Description

The book is devoted to the subject of quantum field theory. It is divided into two volumes. The first volume can serve as a textbook on main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The second edition is extended by additional material, mostly concerning the impact of noncommutative geometry on theories beyond the standard model of particle physics, especially the possible role of torsion in the context of the dark matter problem. Furthermore, the text includes a discussion of the Randall-Sundrum model and the Seiberg-Witten equations.



Mathematical Aspects of Quantum Field Theories

Author : Damien Calaque

Publisher : Springer

Page : 572 pages

File Size : 28,99 MB

Release : 2015-01-06

Category : Science

ISBN : 3319099493

Get eBook

Book Description

Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.