Kavli Affiliate: J. S. Villasenor
| First 5 Authors: J. Fernando Barbero G., Bogar Díaz, Juan Margalef-Bentabol, Eduardo J. S. Villaseñor,
| Summary:
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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