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 study dynamical gauge symmetry breaking via compactified space in the framework of SU(N) gauge theory in M × S (d = 4, 5, 6) space-time. In particular, we study in detail the gauge symmetry breaking in SU(2) and SU(3) gauge theories when the models contain both fundamental and adjoint matter. As a result, we find that any pattern of gauge symmetry breaking can be realized by selecting an app...

The physical phase space in gauge systems is studied. Effects caused by a nonEuclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac gauge invariant states is used to derive a necessary modification of the Hamiltonian path integral in gauge theories of the Yang-Mills type with fermions that ta...

We study gauge fixing in the generalized Gupta-Bleuler quantization. In this method physical states are defined to be simultaneous null eigenstates of a set of quantum invariants. We apply the method to a solvable model proposed by Friedberg, Lee, Pang and Ren and show that no Gribov-type copies appears by construction. Gauge fixing is significant in quantization of gauge theories. Gribov ambig...

‎The purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex Banach space which has a‎ ‎uniformly G^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function ...

According to a recent conjecture, the moduli space of the heterotic conformal field theory on a G ⊂ ADE singularity of an ALE space is equivalent to the moduli space of a pure N = 4 supersymmetric three-dimensional gauge theory with gauge group G. We establish this relation using geometric engineering of heterotic strings and generalize it to theories with non-trivial matter content.