Vacuum Decay in Real Time and Imaginary Time Formalisms

Understand

We analyze vacuum tunneling in quantum field theory in a general formalism by using the Wigner representation.

• In the standard instanton formalism, one usually approximates the initial false vacuum state by an eigenstate of the field operator, imposes Dirichlet boundary conditions on the initial field value, and evolves in imaginary time.
• This approach does not have an obvious physical interpretation.
• However, an alternative approach does have a physical interpretation: in quantum field theory, tunneling can happen via classical dynamics, seeded by initial quantum fluctuations in both the field and its momentum conjugate, which was recently implemented in Ref.