## 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. |

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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 |

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### Common terms and phrases

algebra antifields arbitrary function Batalin bosonic BRST charge BRST invariant BRST transformations canonical Hamiltonian canonical variables canonically conjugate chapter classical commutators configuration space Consider constrained surface construct corresponding defined degrees of freedom denote depend derivatives Dirac brackets embedded equations of motion Euler-Lagrange equations example expression fermion fields formulation Fradkin gauge conditions gauge fixing gauge fixing function gauge identities gauge invariant gauge theories gauge transformations ghost number given Grassmann valued Hamilton equations Hence integration Lagrange multiplier local symmetry master equation matrix nilpotent non-vanishing obtained parameters partition function phase space Phys Poisson brackets primary constraints quantization quantum master equation Rothe second class constraints second class system secondary constraints solution strong involution structure functions symmetry transformations takes the form total action total Hamiltonian transformation laws vanish velocities zero modes φα