Examples of Quantized Field Theories

The following sections are included:

• The Maxwell Field

  • Momentum Representations

  • Fourier Analysis of Operators

  • Emission and Absorption Operators

  • Gauge-Invariance of the Theory

  • The Vacuum State

  • The Gupta-Bleuler Method

  • Example: Spontaneous Emission of Radiation

  • The Hamiltonian Operator

  • Fluctuations of the Fields

  • Fluctuation of Position of an Electron in a Quantized Electromagnetic Field. The Lamb Shift

• Theory of Line Shift and Line Width

  • The Interaction Representation

  • The Application of the Interaction Representation to the Theory of Line-Shift and Line-Width

  • Calculation of Line-Shift, Non-Relativistic Theory

  • The Idea of Mass Renormalization

• Field Theory of the Dirac Electron, Without Interaction

  • Covariant Commutation Rules

  • Momentum Representations

  • Fourier Analysis of Operators

  • Emission and Absorption Operators

  • Charge-Symmetrical Representation

  • The Hamiltonian

  • Failure of Theory with Commuting Fields

  • The Exclusion Principle

  • The Vacuum State

• Field Theory of Dirac Electron in External Field

  • Covariant Commutation Rules

  • The Hamiltonian

  • Antisymmetry of the States

  • Polarization of the Vacuum

  • Calculation of Momentum Integrals

  • Physical Meaning of the Vacuum Polarization

  • Vacuum Polarization for Slowly Varying Weak Fields. The Uehling Effect

• Field Theory of Dirac and Maxwell Fields in Interaction

  • The Complete Relativistic Quantum Electrodynamics

  • Free Interaction Representation