Minimal Proper-time in Quantum Field Theory

TL;DR

This paper introduces a Lorentz-invariant minimal proper time into quantum field theory, leading to high-energy modifications, potential unitarity violations, and a pathway to a finite, asymptotically safe theory.

Contribution

It generalizes quantum field theory by incorporating a minimal proper time, affecting high-energy behavior and unitarity, and providing a framework for a finite, asymptotically safe theory.

Findings

Modifies the Heisenberg uncertainty principle at high energies.

Induces controlled violation of unitarity.

Suppresses high-energy modes and suggests asymptotic safety.

Abstract

We propose a generalization of quantum field theory within Schrodinger's functional representation, inspired by Nambu's proper-time formulation of quantum mechanics. The key motivation for this generalization is to incorporate a fundamental, Lorentz-invariant minimum scale, which in this formulation is played by a minimal proper time $\tau_{\min}$. The introduction of $\tau_{\min}$ leads to several significant effects at very high energies: it modifies the Heisenberg uncertainty principle, induces a controlled violation of unitarity, and suppresses high-energy modes. This minimal scale renders the theory asymptotically safe through a mechanism akin to dimensional reduction, while reproducing all the standard results at low energies, where quantum field theory emerges. Remarkably, the same framework can accommodate a deterministic regime at energies approaching the Planck scale. These features suggest that a minimal proper-time formulation renders the quantum field theory an effective but finite theory, superseded at trans-Planckian energies.