7: Quantization of Relativistic Free Fields

The following sections are included:

• Scalar Fields

  • Real Case

  • Field Quantization

  • Propagator of Free Scalar Particles

  • Complex Case

  • Energy of Free Charged Scalar Particles

  • Behavior under Discrete Symmetries

• Spacetime Behavior of Propagators

  • Wick Rotation

  • Feynman Propagator in Minkowski Space

  • Retarded and Advanced Propagators

  • Comparison of Singular Functions

• Collapse of Relativistic Wave Function

• Free Dirac Field

  • Field Quantization

  • Energy of Free Dirac Particles

  • Lorentz Transformation Properties of Particle States

  • Behavior under Discrete Symmetries

• Free Photon Field

  • Field Quantization

  • Covariant Field Quantization

  • Gupta-Bleuler Subsidiary Condition

  • Behavior under Discrete Symmetries

• Massive Vector Bosons

  • Field Quantization

  • Energy ofMassive Vector Particles

  • Propagator of Massive Vector Particles

• Wigner Rotation of Spin-1 Polarization Vectors

  • Behavior under Discrete Symmetry Transformations

• Spin-3/2 Fields

• Gravitons

• Spin-Statistics Theorem

• CPT-Theorem

• Physical Consequences of Vacuum Fluctuations. Casimir Effect

• Zeta Function Regularization

• Dimensional Regularization

• Accelerated Frame and Unruh Temperature

• Photon Propagator in Dirac Quantization Scheme

• Free Green Functions of n Fields

  • Wick's Theorem

• Functional Form of Wick's Theorem

  • Thermodynamic Version of Wick's Theorem

• Appendix 7A Euler-Maclaurin Formula

• Appendix 7B Liénard-Wiechert Potential

• Appendix 7C Equal-Time Commutator from Time-Ordered Products

• Notes and References