Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 10

Hamiltonian analysis of the BFCG theory for a strict Lie $2$-group

Pages: 3783 – 3800

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n10.a10

Authors

Aleksandar Miković (Departamento de Matemática, Universidade Lusófona, Lisboa, Portugal; and Faculdade de Ciências da Universidade de Lisboa, Portugal)

Miguel Ângelo Oliveira (Faculdade de Ciências da Universidade de Lisboa, Portugal)

Marko Vojinović (Institute of Physics, University of Belgrade, Serbia)

Abstract

We perform a complete Hamiltonian analysis of the BFCG action for a general Lie $2$-group by using the Dirac procedure. We show that the resulting dynamical constraints eliminate all local degrees of freedom which implies that the BFCG theory is a topological field theory.

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A.M. was partially supported by the FCT projects PEst-OE/MAT/UI0208/2013, EXCL/MAT-GEO/0222/2012, and by the bilateral project “Quantum Gravity and Quantum Integrable Models: 2015-2016” (451-03-01765/2014- 09/24) between Portugal and Serbia.

M.A.O. was supported by the FCT grant SFRH/BD/79285/2011.

M.V. was supported by the Science Fund of the Republic of Serbia, grant 7745968, “Quantum Gravity from Higher Gauge Theory 2021” — QGHG-2021.

The contents of this publication are the sole responsibility of the authors and can in no way be taken to reflect the views of the Science Fund of the Republic of Serbia.

Published 25 March 2024