相关论文: A Local Index Formula for the Quantum Sphere
Using the Arthur-Selberg trace formula we express the index of a Dirac operator on an arithmetic quotient over a totally real field with at least two real embeddings as the integral over the index form plus a sum of orbital integrals. For…
It is shown that the square of the Dirac Hamiltonian with the isotropic mass-hedgehog potential in d dimensions is the number operator of fictitious bosons and fermions over d quantum states. This result allows one to obtain the complete…
Quantum particle bound in an infinite, one-dimensional square potential well is one of the problems in Quantum Mechanics (QM) that most of the textbooks start from. There, calculating an allowed energy spectrum for an arbitrary wave…
The coefficients occurring in summation formulae of the Lubbock type are shown to be generalised Bernoulli polynomials which turn up in subdivision questions such as quantum field theory around a conical singularity and on spherical lunes.…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by…
It is shown that the spin operator can be described by an algebra which is in between so(3) and e(2). Relativistic version of the singlet state for two Dirac electrons is discussed. It is shown that a measure of massless particle's…
It is well known that the standard scalar field mimetic cosmology provides a dark matter-like energy density component. Considering $SU(2)$ gauge symmetry, we study the gauge field extension of the mimetic scenario in spatially flat and…
A representation of the quadratic Dirac equation and the Maxwell equations in terms of the three-dimensional universal complex Clifford algebra is given. The investigation considers a subset of the full algebra, which is isomorphic to the…
We study the spectrum of the Dirichlet to Neumann operator of the two-sphere associated to a Schr\"odinger operator in the unit ball. The spectrum forms clusters of size $O(1/k)$ around the sequence of natural numbers $k=1,2,\ldots$, and we…
The quantum algebra suq(2) is introduced as a deformation of the ordinary Lie algebra su(2). This is achieved in a simple way by making use of $q$-bosons. In connection with the quantum algebra suq(2), we discuss the q-analogues of the…
The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…
This paper concerns Fredholm theory in several variables, and its applications to Hilbert spaces of analytic functions. One feature is the introduction of ideas from commutative algebra to operator theory. Specifically, we introduce a…
We consider a quantum dot described by a cylindrically symmetric 2D Dirac equation. The potentials representing the quantum dot are taken to be of different types of potential configuration, scalar, vector and pseudo-scalar to enable us to…
It is shown that the Dirac equation with the Coulomb potential can be solved using the algebra of the three spinor invariants of the Dirac equation without the involvement of the methods of supersymmetric quantum mechanics. The Dirac…
We study the linear cohomological equation in the smooth category over quasi-periodic cocycles in $\mathbb{T} ^{d} \times SU(2)$. We prove that, under a full measure condition on the rotation in $\mathbb{T} ^{d}$, for a generic cocycle in…
In this paper, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and the quasiperiodic boundary conditions. Using these…
The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin…
We propose a new point of view on quantum cohomology, strongly motivated by the work of Givental and Dubrovin, but closer to differential geometry than the existing approaches. The central object is the D-module which "quantizes" a…
We introduce a quantum volume operator $K$ in three--dimensional Quantum Gravity by taking into account a symmetrical coupling scheme of three SU(2) angular momenta. The spectrum of $K$ is discrete and defines a complete set of eigenvectors…