Classical and Quantum Dynamics of Constrained Hamiltonian Systems 1st Edition by Heinz J Rothe, Klaus D Rothe ISBN 9814299642 9789814299640
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Product details:
ISBN 10: 9814299642
ISBN 13: 9789814299640
Author: Heinz J Rothe, Klaus D Rothe
Classical and Quantum Dynamics of Constrained Hamiltonian Systems 1st Table of contents:
1. Introduction
2. Singular Lagrangians and Local Symmetries
2.1 Introduction
2.2 Singular Lagrangians
2.3 Algorithm for Detecting Local Symmetries on Lagrangian Level
2.4 Examples
2.5 Generator of Gauge Transformations and Noether Identities
3. Hamiltonian Approach: The Dirac Formalism
3.1 Introduction
3.2 Primary Constraints
3.3 The Hamilton Equations of Motion
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3.3.1 Streamlining the Hamilton Equations of Motion
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3.3.2 Alternative Derivation of the Hamilton Equations
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3.3.3 Examples
3.4 Iterative Procedure for Generating the Constraints -
3.4.1 Particular Algorithm for Generating the Constraints
3.5 First and Second Class Constraints. Dirac Brackets
4. Symplectic Approach to Constrained Systems
4.1 Introduction
4.2 The Case fabf_{ab}fab Singular
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4.2.1 Example: Particle on a Hypersphere
4.3 Interpretation of W(L)W(L)W(L) and FFF
4.4 The Faddeev-Jackiw Reduction
5. Local Symmetries within the Dirac Formalism
5.1 Introduction
5.2 Local Symmetries and Canonical Transformations
5.3 Local Symmetries of the Hamilton Equations of Motion
5.4 Local Symmetries of the Total and Extended Action
5.5 Local Symmetries of the Lagrangian Action
5.6 Solution of the Recursive Relations
5.7 Reparametrization Invariant Approach
6. The Dirac Conjecture
6.1 Introduction
6.2 Gauge Identities and Dirac’s Conjecture
6.3 General System with Two Primary and One Secondary Constraint
6.4 Counterexamples to Dirac’s Conjecture?
7. BFT Embedding of Second Class Systems
7.1 Introduction
7.2 Summary of the BFT Procedure
7.3 The BFT Construction
7.4 Examples of BFT Embedding
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7.4.1 The Multidimensional Rotator
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7.4.2 The Abelian Self-Dual Model
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7.4.3 Abelian Self-Dual Model and Maxwell-Chern-Simons Theory
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7.4.4 The Non-Abelian SD Model
8. Hamilton-Jacobi Theory of Constrained Systems
8.1 Introduction
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8.1.1 Carathéodory’s Integrability Conditions
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8.1.2 Characteristic Curves of the HJ Equations
8.2 HJ Equations for First Class Systems
8.3 HJ Equations for Second Class Systems -
8.3.1 HPF for Reduced Second Class Systems
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8.3.2 Examples
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8.3.3 HJ Equations for Second Class Systems via BFT Embedding
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8.3.4 Examples
9. Operator Quantization of Second Class Systems
9.1 Introduction
9.2 Systems with Only Second Class Constraints
9.3 Systems with First and Second Class Constraints
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9.3.1 Example: The Free Maxwell Field in the Coulomb Gauge
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9.3.2 Concluding Remark
10. Functional Quantization of Second Class Systems
10.1 Introduction
10.2 Partition Function for Second Class Systems
11. Dynamical Gauges: BFV Functional Quantization
11.1 Introduction
11.2 Grassmann Variables
11.3 BFV Quantization of a Quantum Mechanical Model
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11.3.1 The Gauge-Fixed Effective Lagrangian
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11.3.2 The Conserved BRST Charge in Configuration Space
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11.3.3 The Gauge Fixed Effective Hamiltonian
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11.3.4 The BRST Charge in Phase Space
11.4 Quantization of Yang-Mills Theory in the Lorentz Gauge
11.5 Axiomatic BRST Approach -
11.5.1 The BRST Charge and Hamiltonian for Rank One Theories
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11.5.2 FV Principal Theorem
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11.5.3 A Large Class of Gauges
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11.5.4 Connecting ZZZ with the Quantum Partition Function in a Physical Gauge. The SU(N) Yang-Mills Theory
11.6 Equivalence of the SD and MCS Models
11.7 The Physical Hilbert Space: Some Remarks
12. Field-Antifield Quantization
12.1 Introduction
12.2 Axiomatic Field-Antifield Formalism
12.3 Constructive Proof of the Field-Antifield Formalism for a Restricted Class of Theories
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12.3.1 From the FV-Phase-Space Action to the Hamiltonian Master Equation
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12.3.2 Transition to Configuration Space
12.4 The Lagrangian Master Equation
12.5 The Quantum Master Equation -
12.5.1 An Alternative Derivation of the Quantum Master Equation
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12.5.2 Gauge Invariant Correlation Functions
12.6 Anomalous Gauge Theories: The Chiral Schwinger Model -
12.6.1 Quantum Master Equation and the Anomaly
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