A Statistical Dirac Field Model on Minkowski Spacetime

A statistical field model is constructed on Minkowski spacetime for a self-interacting Dirac field that fluctuates with respect to an auxiliary parameter. The fluctuating Dirac field undergoes a variational Hamiltonian flow while exchanging action with an action bath. Assuming ergodicity, the partition function is calculated and used to provide a perturbative expansion for the field's correlation functions. Non-perturbative calculations are carried out and the resulting 2-point correlation functions have a distinct light cone structure as expected for a relativistic field theory.