Generalized Wavefunctions for Correlated Quantum Oscillators IV: Bosonic and Fermionic Gauge Fields

Abstract

The unitary Clifford algebras are described here for the first time, and arise from the intersection of the orthogonal and common symplectic (Weyl) Clifford algebras of the complexification of the canonical phase space. The convergence of the exponential map is possible in available topologies in our constructions, but it does not converge without additional assumptions in general. Continuous dynamics exists only in semigroups. A well defined spin geometry exists for the unitary Clifford algebras in the appropriate Witt basis, which also affords us both bosonic and fermionic representations through alternative topological completions of the same structure, and physically represent the stable states of the system. Unitary Clifford algebras can be used to define dynamical gauge bundles for arbitrary numbers of correlated (unified) fields. The generic dynamical gauge group for four pairs of canonical variables (four fields) is shown to be isomorphic to $U(4)\times U(4)$, with the spectrum effectively determined by $S[U(4)\times U(3) \times U(1)]$ due to the constraint of geodesic transport of the generators of the dynamical group. This includes prediction of the existence of chimeric bosons, whose quantum numbers are not covariant so they may appear to have a different identity to different observers.