Path Integrals and Periodic Classical Configurations

The following sections are included:

• Introductory Remarks

• The Double Well and Periodic Instantons

  • Periodic configurations and the double well

  • Transition amplitude and Feynman kernel

  • Fluctuations about the periodic instanton

  • The single periodic instanton contribution

  • Sum over instanton–anti-instanton pairs

• The Cosine Potential and Periodic Instantons

  • Periodic configurations and the cosine potential

  • Transition amplitude and Feynman kernel

  • The fluctuation equation and its eigenmodes

  • The single periodic instanton contribution

  • Sum over instanton–anti-instanton pairs

• The Inverted Double Well and Periodic Instantons

  • Periodic configurations and the inverted double well

  • Transition amplitude and Feynman kernel

  • The fluctuation equation and its eigenmodes

  • The single periodic bounce contribution

  • Summing over the infinite number of bounces

• Concluding Remarks