Related papers: Gauge transformations for twisted spectral triples
We construct a spectral-triple framework for a noncommutative planar system associated with a fixed nondegenerate irreducible unitary sector of the kinematical symmetry group $G_{\mathrm{NC}}$, labelled by central parameters…
We update our previous work on the description of twisted configurations for complex massless scalar field on the Kerr black holes as the sections of complex line bundles over the Kerr black hole topology. From physical point of view the…
General Relativity formulated with Noncommutative geometry allows one to obtain, via the fluctuation of Dirac operator, an exact equivalence principle: generation of curvature and torsion from flat space. The fluctuation method presented in…
When aiming to apply mathematical results of non-commutative geometry to physical problems the question arises how they translate to a context in which only a part of the spectrum is known. In this article we aim to detect when a…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
We describe the fully gauge invariant cosmological perturbation equations in teleparallel gravity by using the gauge covariant version of the Stewart lemma for obtaining the variations in tetrad perturbations. In teleparallel theory,…
Complete spectra of the staggered Dirac operator $\Dirac$ are determined in four-dimensional $SU(2)$ gauge fields with and without dynamical fermions. An attempt is made to relate the performance of multigrid and conjugate gradient…
The Moutard transformation for a two-dimensional Dirac operator with a complex-valued potential is constructed. It is showed that this transformation relates the potentials of Weierstrass representations of surfaces related by a composition…
In the literature concerning the monopole matter, three gauges: Dirac, Schwinger, and Wu-Yang's, have been contrasted to each other, and the Wu-Yang's often appears as the most preferable one. The article aims to analyse this view by…
A gauge transformation in quantum electrodynamics involves the product of field operators at the same space-time point and hence does not have a well-defined meaning. One way to avoid this difficulty is to generalize the gauge…
Soon after the Yang-Mills work, the gauge invariance became one of the basic principles in the elementary particles theory. The gauge invariance idea is that Lagrangian has to be invariant not only with respect to the coordinates…
Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that,…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
We develop relative oscillation theory for one-dimensional Dirac operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing…
We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with…
On complete non-compact manifolds with bounded sectional curvature, we consider a class of self-adjoint Dirac-type operators called Dirac-Schr\"odinger operators. Assuming two Dirac-Schr\"odinger operators coincide at infinity, by previous…
In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in momentum space) and with tolerance relations which provide a…
A formula is given in terms of secondary characteristic classes for the leading order contribution to the spectral flow for a path of twisted Dirac operators on an odd dimensional, Riemannian manifold when the twisting is done by a path of…
It has been proposed that the Poincare and some other symmetries of noncommutative field theories should be twisted. Here we extend this idea to gauge transformations and find that twisted gauge symmetries close for arbitrary gauge group.…
Two years ago, we found the supersymmetric counterpart of the spectral triple which specified noncommutative geometry. Based on the triple, we derived gauge vector supermultiplets, Higgs supermultiplets of the minimum supersymmetric…