Null Hamiltonian Yang-Mills theory: Soft symmetries and memory as superselection
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913275206172672 |
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| author | Riello, Aldo Schiavina, Michele |
| author_facet | Riello, Aldo Schiavina, Michele |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03531 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Null Hamiltonian Yang-Mills theory: Soft symmetries and memory as superselection Riello, Aldo Schiavina, Michele Mathematical Physics High Energy Physics - Theory Symplectic Geometry 53D20, 70S15, 70G45, 37K58, 81T13 (Secondary), 58D27 (Secondary), 70S10 (Secondary) 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. |
| title | Null Hamiltonian Yang-Mills theory: Soft symmetries and memory as superselection |
| topic | Mathematical Physics High Energy Physics - Theory Symplectic Geometry 53D20, 70S15, 70G45, 37K58, 81T13 (Secondary), 58D27 (Secondary), 70S10 (Secondary) |
| url | https://arxiv.org/abs/2303.03531 |