Gauge fields with respect to $$d=(3+1)$$ d = ( 3 + 1 ) in the Kaluza–Klein theories and in the spin-charge-family theory

Abstract

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 $$d=(3+1)$$ d = ( 3 + 1 ) space equivalent vector gauge fields, when space with $$d\ge 5$$ d ≥ 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 $$d=(3+1)-g^{\sigma \tau } = \eta ^{\sigma \tau } f^{2}$$ d = ( 3 + 1 ) - g σ τ = η σ τ f 2 – for any scalar function f of the coordinates $$x^{\sigma }$$ x σ , where $$x^{\sigma }$$ x σ denotes the coordinates of space out of $$d=(3+1).$$ d = ( 3 + 1 ) . Also the connection between vielbeins and scalar gauge fields in $$d=(3+1)$$ d = ( 3 + 1 ) (offering the explanation for the Higgs scalar) is discussed.

Keywords

• Scalar Field
• Yukawa Coupling
• Gauge Field
• High Dimensional Space
• Spin Connection