Lorentzian bordisms in algebraic quantum field theory
Mathematical Physics
2025-02-05 v2 High Energy Physics - Theory
Differential Geometry
math.MP
Quantum Algebra
Abstract
It is shown that every algebraic quantum field theory has an underlying functorial field theory which is defined on a suitable globally hyperbolic Lorentzian bordism pseudo-category. This means that globally hyperbolic Lorentzian bordisms between Cauchy surfaces arise naturally in the context of algebraic quantum field theory. The underlying functorial field theory encodes the time evolution of the original theory, but not its spatially local structure. As an illustrative application of these results, the algebraic and functorial descriptions of a free scalar quantum field are compared in detail.
Cite
@article{arxiv.2308.01026,
title = {Lorentzian bordisms in algebraic quantum field theory},
author = {Severin Bunk and James MacManus and Alexander Schenkel},
journal= {arXiv preprint arXiv:2308.01026},
year = {2025}
}
Comments
v2: 34 pages - Final version accepted for publication in Letters in Mathematical Physics