Quantum field theory as a bilocal statistical field theory

TL;DR

This paper introduces a bilocal field reformulation of quantum field theory for bosons, interpreting correlation functions as probabilities and exploring symmetry and unitarity issues at high energies.

Contribution

It presents a novel bilocal field approach to quantum field theory, linking correlation functions to probabilities and analyzing unitarity restoration via renormalization group effects.

Findings

Correlation functions as quantum probabilities

Symmetry treatment similar to traditional formalism

Unitarity violations at high momenta potentially mitigated by fluctuations

Abstract

We develop a reformulation of the functional integral for bosons in terms of bilocal fields. Correlation functions correspond to quantum probabilities instead of probability amplitudes. Discrete and continuous global symmetries can be treated similar to the usual formalism. Situations where the formalism can be interpreted in terms of a statistical field theory in Minkowski space are characterized by violations of unitarity at very large momentum scales. Renormalization group equations suggest that unitarity can be essentially restored by strong fluctuation effects.