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arXiv · 2204.06073

Edge observables of the Maxwell-Chern-Simons theory

J. Fernando Barbero G.·Bogar Díaz·Juan Margalef-Bentabol·Eduardo J. S. Villaseñor
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Abstract

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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J. Fernando Barbero G., Bogar Díaz, Juan Margalef-Bentabol, Eduardo J. S. Villaseñor. 2022-04-12. Edge observables of the Maxwell-Chern-Simons theory. https://doi.org/10.1103/physrevd.106.025011

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