Gauge fields with respect to in the Kaluza–Klein theories and in the spin-charge-family theory

Dragan Lukman; Norma Susana Mankoč Borštnik

doi:10.1140/epjc/s10052-017-4804-y

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2017) 77: 231
https://doi.org/10.1140/epjc/s10052-017-4804-y

Regular Article - Theoretical Physics

Gauge fields with respect to in the Kaluza–Klein theories and in the spin-charge-family theory

Dragan Lukman and Norma Susana Mankoč Borštnik^*

Department of Physics, FMF, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

^* e-mail: norma.mankoc@fmf.uni-lj.si

Received: 31 January 2017
Accepted: 3 April 2017
Published online: 12 April 2017

Abstract

It is shown that in the spin-charge-family theory (Mankoč Borštnik in arXiv:1607.01618v2, 2016, Phys Rev D 91:065004. arxiv:1409.7791, 2015, J Mod Phys 6:2244. doi:10.4236/jmp.2015.615230. arXiv: 1409.4981, 2015, J Mod Phys 4:823. doi:10.4236/jmp.2013.46113. arxiv:1312.1542, 2013, arxiv:1409.4981, 2014) as well as in all the Kaluza–Klein like theories (Blagojević in Gravitation and gauge symmetries, IoP Publishing, Bristol, 2002, An introduction to Kaluza–Klein theories, World Scientific, Singapore, 1983), vielbeins and spin connections manifest in $$d=(3+1)$$ space equivalent vector gauge fields, when space with $d\ge 5$ has a large enough symmetry. The authors demonstrate this equivalence in spaces with the symmetry of the metric tensor in the space out of $d=(3+1)-g^{\sigma \tau } = \eta ^{\sigma \tau } f^{2}$ – for any scalar function f of the coordinates $x^{\sigma }$ , where $x^{\sigma }$ denotes the coordinates of space out of $$d=(3+1).$$ Also the connection between vielbeins and scalar gauge fields in $$d=(3+1)$$ (offering the explanation for the Higgs scalar) is discussed.