Publication: Edge observables of the Maxwell-Chern-Simons theory
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2022-07-15
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American Physical Society (APS)
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We analyze the Lagrangian and Hamiltonian formulations of the Maxwell-Chern-Simons theory defined on a manifold with boundary for two different sets of boundary equations derived from a variational principle. We pay special attention to the identification of the infinite chains of boundary constraints and their resolution. We identify edge observables and their algebra [which corresponds to the well-known U (1) Kac-Moody algebra]. Without performing any gauge fixing, and using the Hodge-Morrey theorem, we solve the Hamilton equations whenever possible. In order to give explicit solutions, we consider the particular case in which the fields are defined on a 2-disk. Finally, we study the Fock quantization of the system and discuss the quantum edge observables and states.
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Barbero G., J. F., Díaz, B., Margalef-Bentabol, J. & Villaseñor, E. J. (2022). Edge observables of the Maxwell-Chern-Simons theory. Physical Review D, 106(2), 025011.