Time evolution with symmetric stochastic action

Understand

Quantum dynamical time-evolution of bosonic fields is shown to be equivalent to a stochastic trajectory in space-time, corresponding to samples of a statistical mechanical steady-state in a higher dimensional quasi-time.

• This is proved using the Q-function of quantum theory with time-symmetric diffusion, that is equivalent to a forward-backward stochastic process in both the directions of time.
• The resulting probability distribution has a positive, time-symmetric action principle and path integral, whose solution corresponds to a classical field equilibrating in an additional dimension.
• Comparisons are made to stochastic quantization and other higher dimensional physics proposals.