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Path Integral and Coherent States in Quantum Mechanics and Field Theory

1. Operator Formalism in the Quantum Mechanics
   • Canonical Quantization
   • Heisenberg Picture
   • Quantum Field Theory
2. Feynman's Path Integration
   • Path Integral in the Quantum Mechanics
     • Representation of the Green's Function in Terms of Path Integral in Phase Space
     • Path Integral in Configuration Space
     • Exercises
   • Path Integral in Quantum Field Theory
3. Coherent States
   • Coherent States of the Harmonic Oscillator
   • Completeness Relation
   • Operators $a^{+},a$ in the Differential Form Representation
4. Holomorphic Path Integral Representation}
   • Common Properties of the Holomorphic Representation
   • Evolution Operator in the Holomorphic Representation
5. Path Integral over Fermi Fields
   • Grassmann Variables
   • Holomorphic Representation of the Fermi Operators
   • Path Integral over Grassmann Variables
   • Dirac Fermionic Field
6. Perturbation Theory and Feynman Graphs}
   • Green's Functions and their Generating Functional
   • Feynman Propagator
   • Propagator of the Relativistic Particle as a Path Integral in the Configuration Space
   • Feynman Rules
   • Momentum Representation
7. Quantum Theory of Abelian Gauge Field
   • Classical Electrodynamics
   • Quantization of the Electromagnetic Field through the Path Integral Method
8. Quantum Theory of Non-Abelian Gauge Field}
   • Yang-Mills Field Theory
   • Canonical Formalism and Path Integral Quantization

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