Stochastic quantization and the role of time in quantum gravity

TL;DR

This paper demonstrates that noncritical string field theory from 2D quantum gravity can be understood through stochastic quantization, linking proper time with stochastic time and providing a nonperturbative quantum Hamiltonian.

Contribution

It introduces a stochastic quantization perspective to noncritical string field theory, connecting proper time with stochastic time and deriving a nonperturbative Hamiltonian.

Findings

Proper time in string theory aligns with stochastic time.

The framework yields a nonperturbative quantum Hamiltonian.

Stochastic time characterizes the proper time in quantum gravity.

Abstract

We show that the noncritical string field theory developed from two-dimensional quantum gravity in the framework of causal dynamical triangulations can be viewed as arising through a stochastic quantization. This requires that the proper time appearing in the string field theory be identified with the stochastic time of the stochastic formulation. The framework of stochastic quantization gives rise to a natural nonperturbative quantum Hamiltonian, which incorporates a sum over all spacetime topologies. We point out that the external character of stochastic time is a feature that pertains more generally to the proper time or distance appearing in nonperturbative correlation functions in quantum gravity.