Related papers: On quantization of Regge links
A modified version of the bilocal particle is presented in terms of complex space time. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac's conjecture.…
In recent years, the picture of discrete space time has been studied in the context of stochastic theory. There are a number of ramifications, which are briefly examined. We argue that the causality of physiics has its roots in the…
The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…
The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asymptotic formula in mathematical physics. Here we give a simple…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
A theory of quantum dynamics based on a discrete structure underlying the space time manifold is developed for single particles. It is shown that at the micro domain the interaction of particles with the underlying discrete structure…
We consider contractions of complexified real cones, as recently introduced by Rugh in [Rugh10]. Dubois [Dub09] gave optimal conditions to determine if a matrix contracts a canonical complex cone. First we generalize his results to the case…
Quantum spectroscopy with single two level systems has considerably improved our ability to detect weak signals. Recently it was realized that for classical signals, precision and resolution of quantum spectroscopy is limited mainly by…
All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
We use recently obtained 2-loop string coupling constants to analyze a class of string models based on orbifold compactification. Assuming weak coupling at the string scale and single-scale unification leads to restrictions on the spectrum…
Canonical quantization of electromagnetic field inside the time--spatially dispersive inhomogeneous dielectrics is presented. Interacting electromagnetic and matter excitation fields create the closed system, Hamiltonian of which may be…
Using the notion of a general conical defect, the Regge Calculus is generalized by allowing for dislocations on the simplicial lattice in addition to the usual disclinations. Since disclinations and dislocations correspond to curvature and…
The diffraction spectrum of an aperiodic solid is related to the group of eigenvalues of the dynamical system associated with the solid. Those eigenvalues with continuous eigenfunctions constitute the topological Bragg spectrum. We relate…
Besides the purely digital or analog interpretation of reality there is a third possibility which incorporates important aspects of both. This is the cyclic formulation of elementary systems, in which elementary particles are represented as…
In this paper we study the perturbative regime in the static patch of de Sitter metric in the Regge-Wheeler formalism. After realizing that perturbative regime in a de Sitter spacetime depicted in terms of usual spherical coordinates cannot…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
DGLAP integro-differential equation can be solved by applying certain map in the complex plane of Mellin moments. It may be re-written as Schr\"odinger equation for $n$ particles. By applying another map in the complex plane of Mellin…
We consider integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of us, extends to…
A singularity $\mathbb{C}^{2r}/G$, with $G$ a split symplectic reflection group, may or may not be crepant. Then the total space $\mathscr{X}$ of the Donagi-Witten integrable system is crepant for some 4d $\mathcal{N}=2$ SCFT and…