Randomness and Irreversibility in Quantum Field Theory

TL;DR

This paper explores how quantum fluctuations induce irreversibility in quantum field theory by analyzing the fractal structure and diffusion of virtual charge distributions generated by quantum corrections.

Contribution

It introduces a statistical interpretation of quantum corrections' virtual charge density and examines its fractal nature and diffusion behavior across different regimes.

Findings

Virtual charge density exhibits fractal structure.

Equilibrium state approaches classical limit regardless of asymptotic freedom.

Diffusion of charge density varies with probing distance.

Abstract

Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range approximation, and adopt for it a statistical interpretation. This virtual charge density has fractal structure, and it is seen that, independently of whether the theory is or is not asymptotically free, it describes a system where the equilibrium state is at its classical limit ($\hbar \rightarrow 0$). We also present a simple analysis of how diffusion of the charge density proceeds as a function of the distance at which the system is probed.