Dynamic coarse-graining approach to quantum field theory

We build quantum field theory on the thermodynamic master equation for dissipative quantum systems. The vacuum is represented by a thermodynamic equilibrium state in the low-temperature limit. All regularization is consistently provided by a friction mechanism; with decreasing friction parameter, only degrees of freedom on shorter and shorter length scales are damped out of a quantum field theory. No divergent integrals need to be manipulated. Renormalization occurs as a tool to refine perturbation expansions, not to remove divergences. Relativistic covariance is recovered in the final results. We illustrate the proposed thermodynamic approach to quantum fields for the ${\phi }^4$ theory by calculating the propagator and the $\beta$ function, and we offer some suggestions on its application to gauge theories.

Figure 1

Feynman diagrams potentially contributing to the propagator in second-order perturbation theory.

Figure 2

Feynman diagrams contributing to the interaction vortex in second-order perturbation theory.

Figure 3

Fixed-point value ${\lambda }^{*}$ of the dimensionless coupling constant resulting from second-order perturbation theory as a function of space dimensionality $d$.