Classical and Quantum Dynamics of Constrained Hamiltonian Systems

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World Scientific, 2010 - Mathematics - 316 pages
This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in nature. Beginning with the early work of Dirac, the book covers the main developments in the field up to more recent topics, such as the field-antifield formalism of Batalin and Vilkovisky, including a short discussion of how gauge anomalies may be incorporated into this formalism. The book is comprehensive and well-illustrated with examples, enables graduate students to follow the literature on this subject without much problems, and to perform research in this field.
 

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Contents

1 Introduction
1
2 Singular Lagrangians and Local Symmetries
6
3 Hamiltonian Approach The Dirac Formalism
24
4 Symplectic Approach to Constrained Systems
51
5 Local Symmetries within the Dirac Formalism
67
6 The Dirac Conjecture
90
7 BFT Embedding of Second Class Systems
108
8 HamiltonJacobi Theory of Constrained Systems
132
11 Dynamical Gauges BFV Functional Quantization
174
12 FieldAntifield Quantization
223
A Local Symmetries and Singular Lagrangians
271
B The BRST Charge of Rank One
278
C BRST Hamiltonian of Rank One
281
D The FV Principal Theorem
283
E BRST Quantization of SU3 YangMills Theory in gauges
287
Bibliography
291

9 Operator Quantization of Second Class Systems
154
10 Functional Quantization of Second Class Systems
164

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