TL;DR
This paper introduces a quantum geometric approach to stochastic quantisation of the Klein-Gordon field, where spacetime is modeled as fuzzy, integrating noise into the background geometry to recover Euclidean space.
Contribution
It develops a novel framework combining fuzzy spacetime with stochastic quantisation, extending the concept of sharp point limits for quantum fields.
Findings
Fuzzy spacetime models Euclidean space in this framework.
The approach successfully reproduces the stochastically quantised Klein-Gordon field.
Provides a new geometric perspective on quantum field quantisation.
Abstract
We present a quantum geometric framework for stochastic quantisation in the case of a free Klein-Gordon field on Euclidean space. In this approach the noise is part of the background space, spacetime is fuzzy. We extend the notion of sharp point limit and show how fuzzy spacetime and the Klein-Gordon field gives the Euclidean space and the stochastically quantised Klein-Gordon field respectively.
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