洛伦兹自由 BV 理论的量子化：因式分解代数与代数量子场论

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-02-26 DOI:10.1007/s11005-024-01784-1

Marco Benini, Giorgio Musante, Alexander Schenkel

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引用次数: 0

摘要

我们构建并比较了 m 维全局双曲洛伦兹流形上自由 BV 理论自然集合的两种可选量子化形式：一种是时序可预因式分解代数，另一种是以共链复数计价的代数量子场论。我们的比较是通过可时序预因子化代数的明确同构来实现的。我们的方法的关键要素是与自由 BV 理论相关的迟滞和高级格林同调，它们将迟滞和高级格林算子泛化为线性微分算子的共链复数。

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Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory

We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of m-dimensional globally hyperbolic Lorentzian manifolds. Our comparison is realized as an explicit isomorphism of time-orderable prefactorization algebras. The key ingredients of our approach are the retarded and advanced Green’s homotopies associated with free BV theories, which generalize retarded and advanced Green’s operators to cochain complexes of linear differential operators.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.