Clifford odd and even objects offer description of internal space of fermions and bosons, respectively, opening new insight into the second quantization of fields

Abstract

In a long series of works the author has demonstrated that the model named the spin-charge-family theory offers the explanation for all in the standard model assumed properties of the fermion and boson fields, as well as for many of their so far observed properties if the space-time is ≥ (13 + 1) while fermions interact with gravity only. In this talk, I briefly report on the so far achievements of the theory. The main contribution demonstrates the offer of the Clifford odd and even objects for the description of the internal spaces of fermion (Clifford odd) and boson (Clifford even) fields, which is opening up a new understanding of the second quantization postulates for the fermion and boson fields: The “basis vectors” determined by the Clifford odd objects demonstrate all the properties of the internal space of fermions and transfer their anti-commutativity to their creation and annihilation operators, while the “basis vectors” determined by the Clifford even objects demonstrate all the properties of the internal space of boson fields and transfer their commutativity to their creation and annihilation operators. The toy model with d = (5 + 1) illustrates the statements.