Related papers: Electrodynamics from Noncommutative Geometry
We examine Podolsky's electrodynamics, which is noninvariant under the usual duality transformation. We deduce a generalization of Hodge's star duality, which leads to a dual gauge field and restores to a certain extent the dual symmetry.…
The most general electrodynamic equations of a perfect conducting state are obtained using a variational principle in a classical framework, following an approach by Pierre-Gilles de Gennes. London equations are derived as the…
We construct the general formulation of N=1 supersymmetric self-dual abelian gauge theory involving auxiliary chiral spinor superfields. Self-duality in this context is just U(N) invariance of the nonlinear interaction of the auxiliary…
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…
It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…
These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
A manifestly gauge-invariant hamiltonian formulation of classical electrodynamics has been shown to be relativistic invariant by the construction of the adequate generators of the Poincare Lie algebra [Physica, 76, No. 3, 421-444 (1974)].…
A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on…
Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea…
Noncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller…
We consider a generalization of Riemannian geometry that naturally arises in the framework of control theory. Let $X$ and $Y$ be two smooth vector fields on a two-dimensional manifold $M$. If $X$ and $Y$ are everywhere linearly independent,…
We lay the foundations for a general approach to nonassociative spectral geometry as an extension of Connes' noncommutative geometry by explaining how to construct finite-dimensional, discrete spectral geometries with exceptional symmetry,…
The theory of a spinor field interacting with a pure Chern-Simons gauge field in 2+1 dimensions is quantized. Dynamical and nondynamical variables are separated in a gauge-independent way. After the nondynamical variables are dropped, this…
We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner Nordstrom like background. The deformation is performed via a particularly chosen Killing twist to ensure that the…
A problem of defining the quantum analogues for semi-classical twists in $U(\mathfrak{g})[[t]]$ is considered. First, we study specialization at $q=1$ of singular coboundary twists defined in $U_{q}(\mathfrak{g})[[t]]$ for $\mathfrak{g}$…
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell…
Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. We study a…
A formulation of classical electrodynamics on an energy-momentum background of constant, non-zero curvature is given. The procedure consists of taking the formulation of standard electrodynamics in the energy-momentum representation, and…
We derive maps relating currents and their divergences in non-abelian U(N) noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. For the U(1) theory, in the slowly-varying-field…