TY - JOUR

T1 - How does Clifford algebra show the way to the second quantized fermions with unified spins, charges and families, and with vector and scalar gauge fields beyond the standard model

T2 - [Inkl. corrigendum]

AU - Borstnik, N. S. Mankoc

AU - Nielsen, H. B.

N1 - Corrigendum: 10.1016/j.ppnp.2022.103961 https://www.sciencedirect.com/science/article/pii/S0146641022000229

PY - 2021/11

Y1 - 2021/11

N2 - Fifty years ago the standard model offered an elegant new step towards understanding elementary fermion and boson fields, making several assumptions, suggested by experiments. The assumptions are still waiting for an explanation. There are many proposals in the literature for the next step. The spin-charge-family theory of one of us (N.S.M.B.) is offering the explanation for not only all by the standard model assumed properties of quarks and leptons and antiquarks and antileptons, with the families included, of the vectors gauge fields, of the Higgs scalar and Yukawa couplings, but also for the second quantization postulates of Dirac and for cosmological observations, like there are the appearance of the dark matter, of matter-antimatter asymmetry, making several predictions. This theory proposes a simple starting action in d >= (13 + 1)-dimensional space with fermions interacting with the gravity only (the vielbeins and the two kinds of the spin connection fields), what manifests in d = (3 + 1) as the vector and scalar gauge fields, and uses the odd Clifford algebra to describe the internal space of fermions, what enables that the creation and annihilation operators for fermions fulfil the anticommutation relations for the second quantized fields without Dirac's postulates: Fermions single particle states already anticommute. We present in this review article a short overview of the spin-charge-family theory, illustrating shortly on the toy model the breaks of the starting symmetries in d = (13+1)-dimensional space, which are triggered either by scalar fields - the vielbeins with the space index belonging to d > (3+1) - or by the condensate of the two right handed neutrinos, with the family quantum number not belonging to the observed families. We compare properties and predictions of this theory with the properties and predictions of SO(10) unifying theories. (C) 2021 Elsevier B.V. All rights reserved.

AB - Fifty years ago the standard model offered an elegant new step towards understanding elementary fermion and boson fields, making several assumptions, suggested by experiments. The assumptions are still waiting for an explanation. There are many proposals in the literature for the next step. The spin-charge-family theory of one of us (N.S.M.B.) is offering the explanation for not only all by the standard model assumed properties of quarks and leptons and antiquarks and antileptons, with the families included, of the vectors gauge fields, of the Higgs scalar and Yukawa couplings, but also for the second quantization postulates of Dirac and for cosmological observations, like there are the appearance of the dark matter, of matter-antimatter asymmetry, making several predictions. This theory proposes a simple starting action in d >= (13 + 1)-dimensional space with fermions interacting with the gravity only (the vielbeins and the two kinds of the spin connection fields), what manifests in d = (3 + 1) as the vector and scalar gauge fields, and uses the odd Clifford algebra to describe the internal space of fermions, what enables that the creation and annihilation operators for fermions fulfil the anticommutation relations for the second quantized fields without Dirac's postulates: Fermions single particle states already anticommute. We present in this review article a short overview of the spin-charge-family theory, illustrating shortly on the toy model the breaks of the starting symmetries in d = (13+1)-dimensional space, which are triggered either by scalar fields - the vielbeins with the space index belonging to d > (3+1) - or by the condensate of the two right handed neutrinos, with the family quantum number not belonging to the observed families. We compare properties and predictions of this theory with the properties and predictions of SO(10) unifying theories. (C) 2021 Elsevier B.V. All rights reserved.

KW - Higher dimensional spaces

KW - Beyond the standard model

KW - Kaluza-Klein-like theories

KW - Fermions representations in Clifford and in

KW - Grassmann space

KW - Second quantization of fermions n Clifford space comparison with Dirac's one

KW - Predictions

KW - FINE-STRUCTURE CONSTANTS

KW - QUARK MASSES

KW - REPRESENTATIONS

KW - DIMENSION

KW - MASSLESS

KW - MATRICES

KW - MIXINGS

KW - ANGLES

U2 - 10.1016/j.ppnp.2021.103890

DO - 10.1016/j.ppnp.2021.103890

M3 - Review

VL - 121

JO - Progress in Particle and Nuclear Physics

JF - Progress in Particle and Nuclear Physics

SN - 0146-6410

M1 - 103890

ER -