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This article presents the description of the internal spaces of fermion andboson 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 propertiesof the corresponding gauge fields. In $d\ge (13+1)$ the corresponding creationoperators manifest in $d=(3+1)$ the properties of all the observed quarks andleptons, with the families included, and of their gauge boson fields, with thescalar fields included, making several predictions. The properties of thecreation and annihilation operators for fermion and boson fields areillustrated on the case $d=(5+1)$, when $SO(5,1)$ demonstrates the symmetry of$SU(3)\times U(1)$.

nuclear physics. b

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}