L. Mangiarotti's Books

Advanced Classical Field Theory

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

Write a review Read reviews Take a Quiz Solve Book Puzzle

Advanced Classical Field Theory

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

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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

393

Publisher

World Scientific

Published Date

ISBN 10

9812838953

ISBN 13

9789812838957

Geometric and Algebraic Topological Methods in Quantum Mechanics

By: G. Giachetta,L. Mangiarotti,Gennadii Aleksandrovich Sardanashvili

Write a review Read reviews Take a Quiz Solve Book Puzzle

Geometric and Algebraic Topological Methods in Quantum Mechanics

By: G. Giachetta,L. Mangiarotti,Gennadii Aleksandrovich Sardanashvili

In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

715

Publisher

World Scientific

Published Date

ISBN 10

9812701265

ISBN 13

9789812701268

Gauge Mechanics

By: L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili

Write a review Read reviews Take a Quiz Solve Book Puzzle

Gauge Mechanics

By: L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili

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. Non-inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads us to observable physics. The gauge formulation of classical mechanics is extended to quantum mechanics under different reference frames. Special topics on geometric BRST mechanics, relativistic mechanics and others, together with many examples, are also dealt with.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

376

Publisher

World Scientific

Published Date

ISBN 10

9810236034

ISBN 13

9789810236038

New Lagrangian and Hamiltonian Methods in Field Theory

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

Write a review Read reviews Take a Quiz Solve Book Puzzle

New Lagrangian and Hamiltonian Methods in Field Theory

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

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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

472

Publisher

World Scientific

Published Date

ISBN 10

9810215878

ISBN 13

9789810215873

Connections in Classical and Quantum Field Theory

By: L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili

Write a review Read reviews Take a Quiz Solve Book Puzzle

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. This collection of basic mathematical facts about various types of connections provides a detailed description of the relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental interactions. This text presents several levels of complexity, from the elementary to the advanced, and provides a considerable number of exercises. 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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

518

Publisher

World Scientific

Published Date

ISBN 10

9812813748

ISBN 13

9789812813749

Book's by L. Mangiarotti

Advanced Classical Field Theory

Advanced Classical Field Theory

Geometric and Algebraic Topological Methods in Quantum Mechanics

Geometric and Algebraic Topological Methods in Quantum Mechanics

Gauge Mechanics

Gauge Mechanics

New Lagrangian and Hamiltonian Methods in Field Theory

New Lagrangian and Hamiltonian Methods in Field Theory

Connections in Classical and Quantum Field Theory

Connections in Classical and Quantum Field Theory

Username

Password

Username

Password

Password again

Birthday

Email