Edge observables of the Maxwell-Chern-Simons theory Articles uri icon

publication date

  • July 2022

start page

  • 025011

issue

  • 2

volume

  • 106

International Standard Serial Number (ISSN)

  • 2470-0010

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.

keywords

  • field theories in lower dimensions; chern-simons theories