Green Hyperbolic Complexes on Lorentzian Manifolds

Benini, Marco; Musante, Giorgio; Schenkel, Alexander

Abstract

We develop a homological generalization of Green hyperbolic operators, called Green hyperbolic complexes, which cover many examples of derived critical loci for gauge-theoretic quadratic action functionals in Lorentzian signature. We define Green hyperbolic complexes through a generalization of retarded and advanced Green’s operators, called retarded and advanced Green’s homotopies, which are shown to be unique up to a contractible space of choices. We prove homological generalizations of the most relevant features of Green hyperbolic operators, namely that (1) the retarded-minus-advanced cochain map is a quasi-isomorphism, (2) a differential pairing (generalizing the usual fiber-wise metric) on a Green hyperbolic complex leads to covariant and fixed-time Poisson structures and (3) the retarded-minus-advanced cochain map is compatible with these Poisson structures up to homotopy.

Citation

Benini, M., Musante, G., & Schenkel, A. (2023). Green Hyperbolic Complexes on Lorentzian Manifolds. Communications in Mathematical Physics, 403, 699-744. https://doi.org/10.1007/s00220-023-04807-5

• Journal Article Type: Article
• Acceptance Date: Jul 3, 2023
• Online Publication Date: Aug 2, 2023
• Publication Date: 2023-10
• Deposit Date: Aug 3, 2023
• Publicly Available Date: Aug 3, 2023
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 403
• Pages: 699-744
• DOI: https://doi.org/10.1007/s00220-023-04807-5
• Keywords: Mathematical Physics; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/23784310
• Publisher URL: https://link.springer.com/article/10.1007/s00220-023-04807-5