Background
Sardanashvily, Gennadi Aleksandre was born on March 13, 1950 in Moscow. Son of Aleksandre and Nadezda (Ustinova) Sardanashvily.
- Photos
- Works
- Photos
- Works
book
New Lagrangian and Hamiltonian Methods in Field Theory
(This work incorporates three modern aspects of mathematic...)
This work incorporates three modern aspects of mathematical physics: the jet methods in differntial geometry, the Lagrangian formalism on jet manifolds and the multimomentum approach to the Hamiltonian formalism. Several contemporary field models are investigated in detail. This is not a book on differential geometry, although modern concepts of differential geometry are used throughout the book. Quadratic Lagrangians and Hamiltonians are studied on the general level including the treatment of Hamiltonian formalism on composite fibre manifolds. The book presents new geometric methods and results in field theory.
http://www.amazon.com/gp/product/9810215878/?tag=2022091-20
Gauge Mechanics
(This text presents in a unified way modern geometric meth...)
This text 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 ion Lagrangian and Hamiltonian formalisms. Non-inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads the reader 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.
http://www.amazon.com/gp/product/9810236034/?tag=2022091-20
Gauge Gravitation Theory
(This concise monograph is intended for students and scien...)
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.
http://www.amazon.com/gp/product/9810207999/?tag=2022091-20
Generalized Hamiltonian Formalism for Field Theory: Constrait Systems
(In the framework of the geometric formulation of field th...)
In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms. The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical moments correspond to derivatives of fields with respect to all world coordinates, not only time. This book is devoted to the application of this formalism to fundamental field models including gauge theory, gravitation theory, and spontaneous symmetry breaking. All these models are constraint ones. Their Euler-Lagrange equations are underdetermined and need additional conditions. In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density. The general procedure for describing constraint systems with quadratic and affine Lagrangian densities is presented.
http://www.amazon.com/gp/product/9810220456/?tag=2022091-20
Connections in Classical and Quantum Field Theory
(Geometrical notions and methods play an important role in...)
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.
http://www.amazon.com/gp/product/9810220138/?tag=2022091-20
Gennadi Aleksandre Sardanashvily
Edit ProfileEducation
Doctor of Philosophy, Moscow State University, 1980; Doctor of Science, Moscow State University, 1998.
Career
Principal research scientist Moscow State University, since 1976.
Achievements
Works
book
-
New Lagrangian and Hamiltonian Methods in Field Theory
(This work incorporates three modern aspects of mathematic...)
-
Connections in Classical and Quantum Field Theory
(Geometrical notions and methods play an important role in...)
-
Gauge Mechanics
(This text presents in a unified way modern geometric meth...)
-
Generalized Hamiltonian Formalism for Field Theory: Constrait Systems
(In the framework of the geometric formulation of field th...)
-
Gauge Gravitation Theory
(This concise monograph is intended for students and scien...)
- Gauge Theory in Jet Manifolds (Hadronic Press Monographs in Applied Mathematics)
-
New Lagrangian and Hamiltonian Methods in Field Theory
Connections
Married Aida Karamysheva, March 19, 1971. Children: Elena, Ira.
