Geometry of Classical Fields

Geometry of Classical Fields
Author :
Publisher : Courier Corporation
Total Pages : 474
Release :
ISBN-10 : 9780486150444
ISBN-13 : 0486150445
Rating : 4/5 (44 Downloads)

Synopsis Geometry of Classical Fields by : Ernst Binz

A canonical quantization approach to classical field theory, this text is suitable for mathematicians interested in theoretical physics as well as to theoretical physicists who use differential geometric methods in their modelling. Introduces differential geometry, the theory of Lie groups, and progresses to discuss the systematic development of a covariant Hamiltonian formulation of field theory. 1988 edition.

Geometry, Symmetries, and Classical Physics

Geometry, Symmetries, and Classical Physics
Author :
Publisher : CRC Press
Total Pages : 702
Release :
ISBN-10 : 9781000530261
ISBN-13 : 1000530264
Rating : 4/5 (61 Downloads)

Synopsis Geometry, Symmetries, and Classical Physics by : Manousos Markoutsakis

This book provides advanced undergraduate physics and mathematics students with an accessible yet detailed understanding of the fundamentals of differential geometry and symmetries in classical physics. Readers, working through the book, will obtain a thorough understanding of symmetry principles and their application in mechanics, field theory, and general relativity, and in addition acquire the necessary calculational skills to tackle more sophisticated questions in theoretical physics. Most of the topics covered in this book have previously only been scattered across many different sources of literature, therefore this is the first book to coherently present this treatment of topics in one comprehensive volume. Key features: Contains a modern, streamlined presentation of classical topics, which are normally taught separately Includes several advanced topics, such as the Belinfante energy-momentum tensor, the Weyl-Schouten theorem, the derivation of Noether currents for diffeomorphisms, and the definition of conserved integrals in general relativity Focuses on the clear presentation of the mathematical notions and calculational technique

Geometry and Quantum Field Theory

Geometry and Quantum Field Theory
Author :
Publisher : American Mathematical Soc.
Total Pages : 476
Release :
ISBN-10 : 0821886835
ISBN-13 : 9780821886830
Rating : 4/5 (35 Downloads)

Synopsis Geometry and Quantum Field Theory by : Daniel S. Freed

The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.

Natural and Gauge Natural Formalism for Classical Field Theorie

Natural and Gauge Natural Formalism for Classical Field Theorie
Author :
Publisher : Springer Science & Business Media
Total Pages : 396
Release :
ISBN-10 : 1402017030
ISBN-13 : 9781402017032
Rating : 4/5 (30 Downloads)

Synopsis Natural and Gauge Natural Formalism for Classical Field Theorie by : L. Fatibene

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.

Gauge Field Theory and Complex Geometry

Gauge Field Theory and Complex Geometry
Author :
Publisher : Springer Science & Business Media
Total Pages : 368
Release :
ISBN-10 : 3540613781
ISBN-13 : 9783540613787
Rating : 4/5 (81 Downloads)

Synopsis Gauge Field Theory and Complex Geometry by : Yuri I. Manin

From the reviews: "... focused mainly on complex differential geometry and holomorphic bundle theory. This is a powerful book, written by a very distinguished contributor to the field" (Contemporary Physics )"the book provides a large amount of background for current research across a spectrum of field. ... requires effort to read but it is worthwhile and rewarding" (New Zealand Math. Soc. Newsletter) " The contents are highly technical and the pace of the exposition is quite fast. Manin is an outstanding mathematician, and writer as well, perfectly at ease in the most abstract and complex situation. With such a guide the reader will be generously rewarded!" (Physicalia) This new edition includes an Appendix on developments of the last 10 years, by S. Merkulov.

Geometry, Particles, and Fields

Geometry, Particles, and Fields
Author :
Publisher :
Total Pages : 668
Release :
ISBN-10 : UCLA:L0065819120
ISBN-13 :
Rating : 4/5 (20 Downloads)

Synopsis Geometry, Particles, and Fields by : Bjørn Felsager

Teil 1: Basic properties of particles and fields. Teil 2: Basic principles and applications of differential geometry

Advanced Classical Field Theory

Advanced Classical Field Theory
Author :
Publisher : World Scientific
Total Pages : 393
Release :
ISBN-10 : 9789812838964
ISBN-13 : 9812838961
Rating : 4/5 (64 Downloads)

Synopsis Advanced Classical Field Theory by : G. Giachetta

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.

Methods Of Differential Geometry In Classical Field Theories: K-symplectic And K-cosymplectic Approaches

Methods Of Differential Geometry In Classical Field Theories: K-symplectic And K-cosymplectic Approaches
Author :
Publisher : World Scientific
Total Pages : 222
Release :
ISBN-10 : 9789814699778
ISBN-13 : 9814699772
Rating : 4/5 (78 Downloads)

Synopsis Methods Of Differential Geometry In Classical Field Theories: K-symplectic And K-cosymplectic Approaches by : Manuel De Leon

This book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism.It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject.

Classical Theory of Gauge Fields

Classical Theory of Gauge Fields
Author :
Publisher : Princeton University Press
Total Pages : 456
Release :
ISBN-10 : 9781400825097
ISBN-13 : 1400825091
Rating : 4/5 (97 Downloads)

Synopsis Classical Theory of Gauge Fields by : Valery Rubakov

Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical or semi-classical level. Accordingly, this book is organized so that its early chapters require no special knowledge of quantum mechanics. Aspects of gauge field theory relying on quantum mechanics are introduced only later and in a graduated fashion--making the text ideal for students studying gauge field theory and quantum mechanics simultaneously. The book begins with the basic concepts on which gauge field theory is built. It introduces gauge-invariant Lagrangians and describes the spectra of linear perturbations, including perturbations above nontrivial ground states. The second part focuses on the construction and interpretation of classical solutions that exist entirely due to the nonlinearity of field equations: solitons, bounces, instantons, and sphalerons. The third section considers some of the interesting effects that appear due to interactions of fermions with topological scalar and gauge fields. Mathematical digressions and numerous problems are included throughout. An appendix sketches the role of instantons as saddle points of Euclidean functional integral and related topics. Perfectly suited as an advanced undergraduate or beginning graduate text, this book is an excellent starting point for anyone seeking to understand gauge fields.

Modern Differential Geometry in Gauge Theories

Modern Differential Geometry in Gauge Theories
Author :
Publisher : Springer Science & Business Media
Total Pages : 303
Release :
ISBN-10 : 9780817644741
ISBN-13 : 0817644741
Rating : 4/5 (41 Downloads)

Synopsis Modern Differential Geometry in Gauge Theories by : Anastasios Mallios

This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable