Clifford algebra as quantum language

TL;DR

This paper proposes using Clifford algebra as a simplified language for quantum dynamics, connecting permutation and rotation representations to quantum fields and spacetime, and suggesting a new perspective on quantum ensembles and history.

Contribution

It introduces Clifford algebra as a novel framework for quantum dynamics, linking permutation groups, spinors, and quantum fields in a unified approach.

Findings

Clifford algebra simplifies quantum dynamics representation.

Quantum fields on quantum spacetime are formulated using Clifford statistics.

Quantum bits of history obey Clifford statistics, implying new computational insights.

Abstract

We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using such representations for their permutations obey Clifford statistics. The vectors supporting the Clifford algebras of permutations and rotations are plexors and spinors respectively. Physical spinors may actually be plexors describing quantum ensembles, not simple individuals. We use Clifford statistics to define quantum fields on a quantum space-time, and to formulate a quantum dynamics-field-space-time unity that evades the compactification problem. The quantum bits of history regarded as a quantum computation seem to obey a Clifford statistics.