Volume 133, Number 6, March 2021
|Number of page(s)||4|
|Section||The Physics of Elementary Particles and Fields|
|Published online||13 May 2021|
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
Received: 4 November 2020
Accepted: 8 March 2021
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.
PACS: 12.10.-g – Unified field theories and models / 02.20.Qs – General properties, structure, and representation of Lie groups / 04.60.-m – Quantum gravity
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