1. Edge observables of the Maxwell-Chern-Simons theory
- Author
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Barbero G., J. Fernando, Díaz, Bogar, Margalef-Bentabol, Juan, Villaseñor, Eduardo J. S., Comunidad de Madrid, Ministerio de Ministerio de Ciencia, Innovación y Universidades (España), Universidad Carlos III de Madrid, European Commission, Ministerio de Ciencia, Innovación y Universidades (España), Atlantic Association for Research in the Mathematical Sciences (Canada), and Natural Sciences and Engineering Research Council of Canada
- Subjects
High Energy Physics - Theory ,Materiales ,High Energy Physics - Theory (hep-th) ,Matemáticas ,Física ,FOS: Physical sciences ,Estadística ,Química ,Mathematical Physics (math-ph) ,Mathematical Physics ,Ingeniería Industrial - Abstract
14 pags., 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., This work has been supported by the Spanish Ministerio de Ciencia Innovación y Universidades-Agencia Estatal de Investigación PID2020–116567GB-C22 grant. B. D. acknowledges support from the CONEX-Plus program funded by Universidad Carlos III de Madrid and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 801538. J. M.-B. is supported by the AARMS postdoctoral fellowship, by the NSERC Discovery Grant No. 2018-04873, and the NSERC Grant No. RGPIN-2018-04887. E. J. S. V. is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation).
- Published
- 2022
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