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

The hamiltonian quantum dynamical structures in the Gel’fand triplets of spaces used in preceding installments to describe correlated hamiltonian dynamics on phase space by quasi-invariant measures are shown to possess a covering structure, which is constructed explicitly using the properties of Clifford algebras. The unitary Clifford algebra is constructed from the intersection of the orthogonal and common symplectic Clifford (Weyl) algebras of the complexification of canonical phase space. Awell defined spin geometry exists for a subset of the symplectic (dynamical) Clifford algebra. The unitary Clifford algebras may provide either bosonic or fermionic representations as alternative topological completions of the same algebraic structure, which represents the stable states of the system. The unitary Clifford algebra is used to define dynamical gauge bundles for two, three and four fields. The canonical dynamical gauge group for four pairs of canonical variables is shown to be SU(4) × SU(3). An isomorphism is shown demonstrating the ability to associate these structures over four pairs of canonical variables with covariant structures in a non-trivial spacetime with (+,−,−,−) local signature.