Spacetime Stochasticity and Second Order Geometry

TL;DR

This paper explores the Schwartz-Meyer second order geometry framework and its application to quantum gravity theories involving spacetime stochasticity, exemplified through Nelson's stochastic quantization.

Contribution

It introduces the relevance of second order geometry to quantum gravity and demonstrates its application via Nelson's stochastic quantization.

Findings

Framework connects second order geometry with quantum gravity concepts

Illustrates the use of stochastic quantization in spacetime models

Provides insights into quantum foam and spacetime stochasticity

Abstract

We discuss the Schwartz-Meyer second order geometry framework and its relevance to theories of quantum gravity that incorporate a notion of spacetime stochasticity or quantum foam. We illustrate the framework in the context of Nelson's stochastic quantization.