Construction and Examples of Higher Gauge Theories∗
Construction and examples of higher gauge theories∗ Tijana Radenkovi´cy Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia Marko Vojinovi´cz Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia Abstract We provide several examples of higher gauge theories, constructed as gener- alizations of a BF model to 2BF and 3BF models with constraints. Using the framework of higher category theory, we introduce appropriate 2-groups and 3- groups, and construct the actions for the corresponding constrained 2BF and 3BF theories. In this way, we can construct actions which describe the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. Each action is naturally split into a topological sector and a sector with simplicity constraints. The properties of the higher gauge group structure opens up a possibility of a nontrivial unification of all fields. 1. Introduction The quantization of the gravitational field is one of the fundamental open problems in modern physics. There are various approaches to this prob- lem, some of which have developed into vast research frameworks. One of such frameworks is the Loop Quantum Gravity approach, which aims to establish a nonperturbative quantization of gravity, both canonically and covariantly [1, 2, 3]. The covariant approach is slightly more general, and ∗ This work was supported by the project ON171031 of the Ministry of Education, Sci- ence and Technological Development (MPNTR) of the Republic of Serbia, and partially by the bilateral scientific cooperation between Austria and Serbia through the project \Causality in Quantum Mechanics and Quantum Gravity - 2018-2019", no.
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