Stochastic quantization and the role of 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.

15 pages

References in corpus (11)

• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Quantum scale invariance, cosmological constant and hierarchy problem
• Scale invariance, unimodular gravity and dark energy
• The Nonperturbative Quantum de Sitter Universe
• Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity
• A String Field Theory based on Causal Dynamical Triangulations
• Quantum Gravity, or The Art of Building Spacetime
• Putting a cap on causality violations in CDT
• Living with Infinities