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Quantum Simulation

On the Kostant-Souriau prequantization of scalar fields with polysymplectic structures

arXiv

Authors: Tom McClain

Year

2024

Paper ID

37117

Status

Preprint

Abstract Read

~2 min

Abstract Words

105

Citations

N/A

Abstract

In this paper, I present a novel, purely differential geometric approach to the quantization of scalar fields, with a special focus on the familiar case of Minkowski spacetimes. This approach is based on using the natural geometric structures of polysymplectic Hamiltonian field theory to produce an analog of the Kostant-Souriau prequantization map familiar from geometric quantization. I show that while the resulting operators are quite different from those of canonical quantum field theory, the approach is nonetheless able to reproduce a few of canonical quantum field theory's most fundamental results. I finish by elaborating the current limitations of this approach and briefly discussing future prospects.

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In this paper, I present a novel, purely differential geometric approach to the quantization of scalar fields, with a special focus on the familiar case of Minkowski spacetimes.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2411.04087 [2] arXiv https://arxiv.org/abs/2411.04087 [3] Publisher https://arxiv.org/abs/2411.04087

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