Standard Model and 4-groups

¹ Departamento de Matemática e COPELABS, Universidade Lusófona de Humanidades e Tecnologias Av. do Campo Grande, 376, 1749-024 Lisboa, Portugal
² Grupo de Física Matemática da Universidade de Lisboa, Faculdade de Ciências - Campo Grande, Edifício C6, PT-1749-016 Lisboa, Portugal
³ Institute of Physics, University of Belgrade - Pregrevica 118, 11080 Belgrade, Serbia

^(a) amikovic@ulusofona.pt
^(b) vmarko@ipb.ac.rs

Received: 4 November 2020
Accepted: 8 March 2021

Abstract

We show that a categorical generalization of the the Poincaré symmetry which is based on the n-crossed modules becomes natural and simple when n = 3 and that the corresponding 3-form and 4-form gauge fields have to be a Dirac spinor and a Lorentz scalar, respectively. Hence by using a Poincaré 4-group we naturally incorporate fermionic and scalar matter into the corresponding 4-connection. The internal symmetries can be included into the 4-group structure by using a 3-crossed module based on the group, so that for we can include the Standard Model into this categorification scheme.