A new perspective on quantum field theory revealing possible existence of another kind of fermions forming dark matter

Abstract

Quantum fields are considered as generators of infinite-dimensional Clifford algebra [Formula: see text], which can be either orthogonal (in the case of fermions) or symplectic (in the case of bosons). A generic quantum state can be expressed as a superposition of the basis elements of [Formula: see text], with the superposition coefficients being multiparticle complex-valued wavefunctions. The basis elements, that are products of the generators of [Formula: see text] in the Witt basis, act as creation and annihilation operators. They create positive and negative energy states that include the bare and the Dirac vacuum as special cases. It is shown that the nonvanishing electric charge arises from an extra dimension or from doubling the number of creation and annihilation operators, which brings an extra imaginary unit [Formula: see text] into the description. A further extension is to consider [Formula: see text] as one of the quaternionic imaginary units and consider a generic state as having values in the quaternionic algebra or, equivalently, in the complexified two-dimensional Clifford algebra, [Formula: see text]. It contains two distinct fundamental representations of [Formula: see text], one associated with the weak isospin doublet [Formula: see text] and the other one with the doublet of new leptons, denoted by [Formula: see text], that together with the new quarks [Formula: see text] can be identified with dark matter.