Null Hamiltonian Yang-Mills theory: Soft symmetries and memory as superselection
| Autor: | Riello, Aldo, Schiavina, Michele |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Ann. Henri Poincar\'e (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00023-024-01428-z |
| Popis: | Soft symmetries for Yang-Mills theory are shown to correspond to the residual Hamiltonian action of the gauge group on the Ashtekar-Streubel phase space, which is the result of a partial symplectic reduction. The associated momentum map is the electromagnetic memory in the abelian theory, or a nonlinear, gauge-equivariant, generalization thereof in the nonabelian case. This result follows from an application of Hamiltonian reduction by stages, enabled by the existence of a natural normal subgroup of the gauge group on a null codimension-1 submanifold with boundaries. The first stage is coisotropic reduction of the Gauss constraint, and it yields a symplectic extension of the Ashtekar-Streubel phase space (up to a covering). Hamiltonian reduction of the residual gauge action leads to the fully-reduced phase space of the theory. This is a Poisson manifold, whose symplectic leaves, called superselection sectors, are labelled by the (gauge classes of the generalized) electric flux across the boundary. In this framework, the Ashtekar-Streubel phase space arises as an intermediate reduction stage that enforces the superselection of the electric flux at only one of the two boundary components. These results provide a natural, purely Hamiltonian, explanation of the existence of soft symmetries as a byproduct of partial symplectic reduction, as well as a motivation for the expected decomposition of the quantum Hilbert space of states into irreducible representations labelled by the Casimirs of the Poisson structure on the reduced phase space. Comment: 52 pages + Appendices. New on v4 (accepted version): Added subsection 1.4 and a 'notation summary' (appendix F). Slight improvements throughout, slight title change |
| Databáze: | arXiv |
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