Classical and Quantum Dynamics of Constrained Hamiltonian SystemsThis 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. |
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 |
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Common terms and phrases
action algebra algorithm arbitrary associated Batalin BRST canonical canonical Hamiltonian chapter choice classical commutators Consider construct coordinates corresponding defined denote depend derivatives described determined Dirac brackets discussed dynamics embedded equations of motion equivalent example exists expression fact fermion fields finds formulation gauge fixing gauge identities gauge invariant gauge theories ghost given Grassmann Hamilton equations Hamiltonian Hence implemented implies independent infinitesimal integration introduce involving Lagrange Lagrangian leads master equation matrix momenta multiplier Note observables obtained operator parameters particular partition function phase space Phys Poisson brackets primary constraints quantization quantum quantum mechanical reduced relations replaced requirement respect Rothe satisfy second class second class constraints second class system secondary constraints singular solution structure surface symmetry theory transformations vanish variables variation written zero modes