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, ...

We study the quantum group gauge theory developed elsewhere in the limit when the base space (spacetime) is a classical space rather than a general quantum space. We show that this limit of the theory for gauge quantum group Uq(g) is isomorphic to usual gauge theory with Lie algebra g. Thus a new kind of gauge theory is not obtained in this way, although we do find some differences in the coupl...

The bundle structure of the space A of Ashtekar’s generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the generic stratum. Its structure group equals the space G of all generalized gauge transforms modulo the constant center-valued gauge transforms. For abelian gauge th...

We consider chiral gauge theories defined over a fixed four-dimensional space-time manifold with a Cartesian product structure for at least one compact spatial dimension, e.g. the product of Minkowskian 3-space and a circle. For a simple set-up, we calculate the effective gauge field action obtained from integrating out the chiral fermions, while maintaining gauge invariance. Due to a combinati...

We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...