14: Functional-Integral Representation of Quantum Field Theory

The following sections are included:

• Functional Fourier Transformations

• Gaussian Functional Integral

• Functional Formulation for Free Quantum Fields

• Interactions

• Euclidean Quantum Field Theory

• Functional Integral Representation for Fermions

• Relation Between Z[j] and the Partition Function

• Bosons and Fermions in a Single State

• Free Energy of Free Scalar Fields

• Interacting Nonrelativistic Fields

  • Functional Formulation

  • Grand-Canonical Ensembles at Zero Temperature

• Interacting Relativistic Fields

• Plasma Oscillations

  • General Formalism

  • Physical Consequences

• Pair Fields

• Competition of Plasmon and Pair Fields

• Ambiguity in the Selection of Important Channels

• Gauge Fields and Gauge Fixing

• Nontrivial Gauge and Faddeev-Popov Ghosts

• Functional Formulation of Quantum Electrodynamics

  • Decay Rate of Dirac Vacuum in Electromagnetic Fields

  • Constant Electric and Magnetic Background Fields

  • Decay Rate in a Constant Electromagnetic Field

  • Effective Action in a Purely Magnetic Field

  • Effective Action in a Purely Magnetic Field

  • Effective Action in a Purely Magnetic Field

  • Heisenberg-Euler Lagrangian

  • Alternative Derivation for a Constant Magnetic Field

• Appendix 14A Propagator of the Bilocal Pair Field

• Appendix 14B Fluctuations around the Composite Field

• Appendix 14C Two-Loop Heisenberg-Euler Effective Action

• Notes and References