Symplectic quantization I: dynamics of quantum fluctuations in a relativistic field theory

TL;DR

This paper introduces a novel symplectic quantization method for scalar field theories, linking quantum fluctuations to relativistic invariance and action-based equiprobability, enabling analysis of both equilibrium and non-equilibrium dynamics.

Contribution

It proposes a new symplectic quantization scheme that incorporates a proper time for non-equilibrium analysis, extending stochastic quantization with a symplectic evolution framework.

Findings

Defines a symplectic evolution in action space

Allows study of non-equilibrium transient dynamics

Links quantum fluctuations to relativistic invariance

Abstract

We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This proper time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in the companion work "Symplectic quantization II".