Related papers: Hypergeometric Connotations of Quantum Equations
This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of noncommutative supergeometry in harmonic…
Two non-standard quantum deformations of the (1+1) Schr\"odinger algebra are identified with the symmetry algebras of either a space or time uniform lattice discretization of the Schr\"odinger equation. For both cases, the deformation…
We develop a theory of the Klein-Gordon equation on curved spacetimes. Our main tool is the method of (non-autonomous) evolution equations on Hilbert spaces. This approach allows us to treat low regularity of the metric, of the…
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
It has been known for some time that the cosmological Friedmann equation deduced from General Relativity can be also obtained within the Newtonian framework under certain assumptions. We use this result together with quantum corrections to…
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to…
We consider nonlinear Klein-Gordon wave equations and illustrate that standard discretizations thereof (involving nearest neighbors) may preserve either standardly defined linear momentum or total energy but not both. This has a variety of…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
We establish that solutions, to the most simple NLKG equations in 2 space dimensions with mass resonance, exhibits long range scattering phenomena. Modified wave operators and solutions are constructed for these equations. We also show that…
Two sets of super Riccati equations are presented which result in two linear problems of super sine-Gordon equation. The linear problems are then shown to be related to each other by a super gauge transformation and to the super…
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum…
In this article one will discuss the system of coupled nonlinear Klein-Gordon equations with different velocities and different masses. The nonlinearity considered is a general quadratic nonlinearity without any restriction. The method is a…
Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.
The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…
Using the elementary axioms of special relativity and quantum mechanics we construct a wave equation which generalizes the Schrodinger equation. We also solve the general second and some higher order differential equations.
In this paper, we consider the long time behavior of solution to the quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space dimensions. For a given asymptotic profile, we construct a solution to (NLKG) which converges…
The generic shape of the single-time and two-time correlators in non-equilibrium phase-ordering kinetics with ${z}=2$ is obtained from the co-variance of the four-point response functions. Their non-equilibrium scaling forms follow from a…
In this paper we show that the one-dimensional Schr\"odinger equation can be viewed as the geodesic equation of a certain metric on a 2-surface. In case of the Schr\"odinger equation with a finite-gap potential, the metric and geodesics are…
We introduce a class of pseudo-bosonic Klein-Gordon fields in 1+1 dimensions and we discuss some of their properties. This work originates from non Hermitian quantum mechanics and deformed canonical commutation relations. We show that,…