How Clifford algebra helps understand second quantized quarks and leptons and corresponding vector and scalar boson fields, {\it opening a new step beyond the standard model}

Abstract

This article presents the description of the internal spaces of fermion and boson fields in $d$-dimensional spaces, with the odd and even "basis vectors" which are the superposition of odd and even products of operators ${\gamma }^a$. While the Clifford odd "basis vectors" manifest properties of fermion fields, appearing in families, the Clifford even "basis vectors" demonstrate properties of the corresponding gauge fields. In $d\ge (13+1)$ the corresponding creation operators manifest in $d=(3+1)$ the properties of all the observed quarks and leptons, with the families included, and of their gauge boson fields, with the scalar fields included, making several predictions. The properties of the creation and annihilation operators for fermion and boson fields are illustrated on the case $d=(5+1)$, when $SO(5,1)$ demonstrates the symmetry of $SU(3)\times U(1)$.

42 pages. arXiv admin note: substantial text overlap with arXiv:2210.07004, arXiv:2210.06256

References in corpus (3)

• 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 {\it standard model}
• Are superheavy stable quark clusters viable candidates for the dark matter?
• Clifford odd and even objects offer the description of the internal space of fermions and bosons, respectively, opening new insight into the second quantization of fields

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