Probing the scale of non-commutativity of space

TL;DR

This paper investigates the implications of non-commutative space in quantum electrodynamics, revealing constraints on charge quantization and composite operators, and setting limits on the non-commutativity scale based on collider data.

Contribution

It demonstrates that non-commutative spaces impose specific restrictions on charge and composite operators, and derives bounds on the non-commutativity scale from experimental data.

Findings

Charge g is allowed only as the basic NC photon coupling.

Composite operators lack simple transformation properties.

Non-commutativity scale is constrained below current LHC limits.

Abstract

Examining quantum electrodynamics in non-commutative (NC) spaces along with composite operators in these spaces, we show that i) any charge g for a fermion matter field is allowed provided the basic NC photon-photon coupling is g, however no other multiples of g are permitted and ii) composite operators do not have a simple transformation which can be attributed to the effective total charge of the composite particle. Taken together these results place a limit on the scale of non-commutativity to be at most smaller that current LHC limits for compositeness. Furthermore, they also suggest that a substructure at still smaller scales is needed if such spaces are to be a physical reality.