On Computable Geometric Expressions in Quantum Theory

TL;DR

This paper establishes criteria for the computability of geometric algebra expressions within quantum theory, ensuring their algebraic properties are preserved during transformations, with implications for dynamical multivector fields.

Contribution

It introduces specific criteria for the computability of geometric algebra expressions in quantum theory, linking algebraic transformations to physical properties.

Findings

Criteria for basis transformations in geometric algebra within quantum theory

Implications for the physics of dynamical multivector fields

Preservation of algebraic properties during transformations

Abstract

Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in quantum theory, in such a way that preserves their algebraic properties. They are that one must be able to arbitrarily transform the basis of the Clifford algebra, via multiplication by elements of the algebra that act trivially on the state space; all such elements must be neighbored by operators corresponding to factors in the original expression and not the state vectors. We explore the consequences of these criteria for a physics of dynamical multivector fields.