Testing Non-commutative QED, Constructing Non-commutative MHD

TL;DR

This paper explores the implications of non-commutative geometry on electromagnetic wave propagation and fluid dynamics, proposing potential experimental tests and constructing a non-commutative magnetohydrodynamics theory.

Contribution

It introduces a framework for testing non-commutative QED effects via Lorentz invariance violation and develops a non-commutative MHD theory for charged fluids in strong magnetic fields.

Findings

Non-commutativity causes anisotropic wave velocities.

Potential experimental test via Michelson-Morley interference.

Constructs a non-commutative fluid dynamics model.

Abstract

The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into their lowest Landau level and renders the fluid dynamics non-commutative, with a Moyal product determined by the background magnetic field.