Renormalizability of semiquantized fields

TL;DR

This paper investigates the renormalizability of semiquantized fields within stochastic quantization, revealing that such theories are generally less renormalizable than fully quantized theories and are unphysical due to broken reflection positivity.

Contribution

It introduces a framework for analyzing the dynamics of classical and quantum interacting systems in stochastic quantization and assesses their renormalizability.

Findings

The theory breaks reflection positivity, making it unphysical.

Semiquantized theories are less renormalizable than fully quantized ones.

Derived Feynman rules for Euclidean vacuum expectation values.

Abstract

A definition is given, in the framework of stochastic quantization, for the dynamics of a system composed of classical and quantum degrees of freedom mutually interacting. It is found that the theory breaks reflection positivity, and hence it is unphysical. The Feynman rules for the Euclidean vacuum expectation values are derived and the perturbative renormalizability of the theory is analyzed. Contrary to the naive expectation, the semiquantized theory turns out to be less renormalizable, in general, than the corresponding completely quantized theory.