Gennadi A Sardanashvily's Books

Connections in Classical and Quantum Field Theory

By: L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili

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Connections in Classical and Quantum Field Theory

By: L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.

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Page Count

516

Publisher

World Scientific

Published Date

ISBN 10

9810220138

ISBN 13

9789810220136

Advanced Classical Field Theory

By: Giovanni Giachetta,Gennadi A Sardanashvily,Luigi Mangiarotti

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Advanced Classical Field Theory

By: Giovanni Giachetta,Gennadi A Sardanashvily,Luigi Mangiarotti

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 — gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory — 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.

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Page Count

393

Publisher

World Scientific

Published Date

ISBN 10

9814468649

ISBN 13

9789814468640

Gauge Mechanics

By: Luigi Mangiarotti,Gennadi A Sardanashvily

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Gauge Mechanics

By: Luigi Mangiarotti,Gennadi A Sardanashvily

This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads us to observable physics. Special topics on relativistic mechanics, geometric BRST mechanics frame-dependent quantization and others, together with many examples, are also dealt with.

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Page Count

366

Publisher

World Scientific

Published Date

ISBN 10

9814495689

ISBN 13

9789814495684

New Lagrangian And Hamiltonian Methods In Field Theory

By: Giovanni Giachetta,Luigi Mangiarotti,Gennadi A Sardanashvily

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New Lagrangian And Hamiltonian Methods In Field Theory

By: Giovanni Giachetta,Luigi Mangiarotti,Gennadi A Sardanashvily

This book incorporates 3 modern aspects of mathematical physics: the jet methods in differential geometry, Lagrangian formalism on jet manifolds and the multimomentum approach to Hamiltonian formalism. Several contemporary field models are investigated in detail.This is not a book on differential geometry. However, modern concepts of differential geometry such as jet manifolds and connections are used throughout the book. Quadratic Lagrangians and Hamiltonians are studied at the general level including a treatment of Hamiltonian formalism on composite fiber manifolds. The book presents new geometric methods and results in field theory.

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Page Count

466

Publisher

World Scientific

Published Date

ISBN 10

9814518085

ISBN 13

9789814518086

Gravity, Particles and Space-time

By: Petr Ivanovich Pronin,Gennadi? Aleksandrovich Sardanashvili

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Gravity, Particles and Space-time

By: Petr Ivanovich Pronin,Gennadi? Aleksandrovich Sardanashvili

This volume comprises original and review articles on the frontier problems of the gravitation theory, theoretical and mathematical physics. The volume is dedicated to the memory of Professor Dmitri Ivanenko who made the great contribution to the physical science of the twentieth century.

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Page Count

536

Publisher

World Scientific

Published Date

ISBN 10

9810226683

ISBN 13

9789810226688

Geometric and Algebraic Topological Methods in Quantum Mechanics

By: G. Giachetta,L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili

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Geometric and Algebraic Topological Methods in Quantum Mechanics

By: G. Giachetta,L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili

- The book collects all the advanced methods of quantization in the last decade. - It presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.

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Page Count

716

Publisher

World Scientific

Published Date

ISBN 10

9812561293

ISBN 13

9789812561299

Geometric Formulation of Classical and Quantum Mechanics

By: G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili

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Geometric Formulation of Classical and Quantum Mechanics

By: G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili

The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

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Page Count

405

Publisher

World Scientific

Published Date

ISBN 10

9814313726

ISBN 13

9789814313728

Noether's Theorems

Applications in Mechanics and Field Theory

By: Gennadi Sardanashvily

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Noether's Theorems

Applications in Mechanics and Field Theory

By: Gennadi Sardanashvily

The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.

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Page Count

304

Publisher

Springer

Published Date

ISBN 10

9462391718

ISBN 13

9789462391710

Gauge Gravitation Theory

By: Gennadi? Aleksandrovich Sardanashvili,O. Zakharov

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Gauge Gravitation Theory

By: Gennadi? Aleksandrovich Sardanashvili,O. Zakharov

This concise monograph is intended for students and scientists specializing in contemporary field theory, gravitation theory and modern differential geometry. The gauge theory as presented by the authors, incorporates Einstein's gravity into the universal picture of fundamental interactions and clarifies its physical nature as a Higgs field. A key point advanced here is the spontaneous breakdown of space-time symmetries according to the equivalence principle. The jet manifold generalization of the fibre bundle machinery is used to describe this symmetry breaking, degenerate Hamiltonian systems and general connections.

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Page Count

134

Publisher

World Scientific

Published Date

ISBN 10

9810207999

ISBN 13

9789810207991

Book's by Gennadi A Sardanashvily

Connections in Classical and Quantum Field Theory

Connections in Classical and Quantum Field Theory

Advanced Classical Field Theory

Advanced Classical Field Theory

Gauge Mechanics

Gauge Mechanics

New Lagrangian And Hamiltonian Methods In Field Theory

New Lagrangian And Hamiltonian Methods In Field Theory

Gravity, Particles and Space-time

Gravity, Particles and Space-time

Geometric and Algebraic Topological Methods in Quantum Mechanics

Geometric and Algebraic Topological Methods in Quantum Mechanics

Geometric Formulation of Classical and Quantum Mechanics

Geometric Formulation of Classical and Quantum Mechanics

Noether's Theorems

Noether's Theorems

Gauge Gravitation Theory

Gauge Gravitation Theory

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