Momentum Gauge Fields and Non-Commutative Space-Time

Abstract

In this work we present a gauge principle that starts with the momentum space representation of the position operator (${\hat{x}}_i=i\hslash \frac{\partial }{\partial p_i}$) rather than starting with the position space representation of the momentum operator (${\hat{p}}_i=-i\hslash \frac{\partial }{\partial x_i}$). We discuss some simple examples with this new type of gauge theory: (i) analog solutions from ordinary gauge theory in this momentum gauge theory, (ii) Landau levels using momentum gauge fields, (iii) the emergence of non-commutative space-times from the momentum gauge fields. We find that the non-commutative space-time parameter can be momentum dependent, and one can construct a model where space-time is commutative at low momentum but becomes non-commutative at high momentum.

17 pages, this last version is to appear in the Symmetry in the Steven Weinberg Memorial special issue, discussion on mixing between momentum and ordinary magnetic fields and the relation with analogous mixings in the standard model that define photon and Z boson has been added

References in corpus (2)

• Covariant formulation of Generalised Uncertainty Principle
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction

Cited by in corpus (4)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Classical and quantum bicosmology with noncommutativity
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
• Emergent spacetime from a Berry-inspired dynamical gauge field coupled to electromagnetism