A two-dimensional observable is a special kind of a σ-homomorphism defined on the Borel σ-algebra of the real plane with values in a σ-complete MV-algebra or in a monotone σ-complete effect algebra. A two-dimensional spectral resolution is a mapping defined on the real plane with values in a σ-complete MV-algebra or in a monotone σ-complete effect algebra which has properties similar to a two-dimensional

We prove, in this paper, the well-posedness and nonnegativity of the regular solution of the relativistic Boltzmann equation in the presence of a given electromagnetic field, taking as background a Lorentzian space-time which is of type Bianchi I with locally rotational symmetry.

Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. it is postulated that a quantum observable corresponds to a unitary representation of an abelian Lie group, the irreducible subrepresentations of which correspond to the observable's outcomes. It

The purpose of this article is to give a result of localization in position space of the photons in the ground state for a Hamiltonian describing nuclear magnetic resonance in quantum electrodynamics. We prove that |x|−5 is an upper bound of the photon number density as |x| goes to infinity. We also obtain the asymptotic behaviour of the photon number at infinity and prove in particular that it is

In this paper we consider magnetic Schrödinger operators on the two-dimensional unit disk with a radially symmetric magnetic field which explodes to infinity at the boundary. We prove a bound for the eigenvalue moments and a bound for the number of negative eigenvalues for such operators.

We discuss a few models of quantum universal enveloping algebra Uq(sl(2)) from the q-special matrix functions point of view. These models are in terms of q-dilation operators and matrix q-difference-dilation operators and are connected through a matrix q-integral transformation. In the process, we find new basic matrix function identities involving one and two variable q-special matrix functions.

In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain closed analytic expressions for the form factors, the Debye functions and their asymptotic decay. The relation between the end-to-halftime and radius of gyration is computed for these classes of periodic processes.

The results for Fisher information of the Morse oscillator have thus far been reported [8] for only the ground state of the system. We make use of the wave functions in [21] to provide a general method for computing Fisher-information values for both bound and excited states of the potential. In order to visualize the effects of anharmonicity, the results of the position- and momentum-space Fisher

We present an application of the Schur–Weyl duality in the one-dimensional Hubbard model in the case of a half-filled system of any number of atoms. We replace the actions of the dual symmetric and unitary groups in the whole 4N-dimensional Hilbert space by the actions of the dual groups in the spin and pseudo-spin spaces. The calculations significantly reduce the dimension of the eigenproblem of the