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Introduction to a Quantum Impedance Model

P. Cameron

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Two fundamental conceptual structures have been lost in quantum mechanics - geometric representation of Clifford algebra and quantization of wavefunction interaction impedances. This presentation outlines their histories and how their synthesis opens a new window on the standard model.
DOI
10.13140/rg.2.2.20650.75209

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Projection operators are central to the algebraic formulation of quantum theory because both wavefunction and hermitian operators(observables) have spectral decomposition in terms of the spectral projections. Projection operators are hermitian operators which are idempotents also. We call them quantum idempotents. They are also important for the conceptual understanding of quantum theory because projection operators also represent observation process on quantum system. In this paper we explore the algebra of quantum idempotents and show that they generate Iterant algebra (defined in the paper), Lie algebra, Grassmann algebra and Clifford algebra which is very interesting because these later algebras were introduced for the geometry of spaces and hence are called geometric algebras. Thus the projection operator representation gives a new meaning to these geometric algebras in that they are also underlying algebras of quantum processes and also they bring geometry closer to the quantum theory. It should be noted that projection operators not only make lattices of quantum logic but they also span projective geometry. We will give iterant representations of framed braid group algebras, parafermion algebras and the su(3)su(3)su(3) algebra of quarks. These representations are very striking because iterant algebra encodes the spatial and temporal aspects of recursive processes. In that regard our representation of these algebras for physics opens up entirely new perspectives of looking at fermions,spins and parafermions(anyons).