Momentum Gauge Fields and Non-Commutative Space–Time

In this work, we present a gauge principle that starts with the momentum space representation of position operator (x^i=iℏ∂∂pi), rather than starting (p^i=−iℏ∂∂xi). This extension can be seen as dynamical version Born’s reciprocity theory, which exchanges and momentum. We discuss some simple examples new type theory: (i) analog solutions from ordinary theory in (ii) Landau levels using fields, (iii) emergence non-commutative space–times fields. find space–time parameter dependent, one construct model where is commutative at low momentum, but becomes high