2025/07/27 by Gudder, Stan
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2507.20394
Corresponding to a finite dimensional Hilbert space H with dim H=n, we define a geometric algebra \gscript (H) with dim\sqbrac\gscript (H)=2n. The algebra \gscript (H) is a Hilbert space that contains H as a subspace. We interpret the unit vectors of H as states of individual fermions of the same type and \gscript (H) as a fermion quantum field whose unit vectors represent states of collections of interacting fermions. We discuss creation operators on \gscript (H) and provide their matrix representations. Evolution operators provided by self-adjoint Hamiltonians on H and \gscript (H) are considered. Boson-Fermion quantum fields are constructed. Extensions of operators from H to \gscript (H) are studied. Finally, we present a generalization of our work to infinite dimensional separable Hilbert spaces.