Related papers: Truncated su(2) moment problem for spin and polari…
In this paper we study truncated moment problems for $J$-self-adjoint, $J$-skew-self-adjoint and $J$-unitary operators. Conditions of the solvability are given. Some canonical solutions of the moment problems are constructed. As a…
We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. A way to construct atomic solutions of the moment problem is indicated.
We investigate the structure of SO(3)-invariant quantum systems which are composed of two particles with spins j_1 and j_2. The states of the composite spin system are represented by means of two complete sets of rotationally invariant…
In this paper we study the truncated operator trigonometric moment problem. All solutions of the moment problem are described by a Nevanlinna-type parameterization. In the case of moments acting in a separable Hilbert space, the matrices of…
In this paper we study the truncated matrix trigonometric moment problem. We obtained a bijective parameterization of all solutions of this moment problem (both in nondegenerate and degenerate cases) via an operator approach. We use…
In this paper we consider a problem of the similarity of complex symmetric operators to perturbations of restrictions of normal operators. For a subclass of cyclic complex symmetric operators in a finite-dimensional Hilbert space we prove…
In this paper we obtain a description of all solutions of truncated matricial moment problems on a finite interval in a general case (no conditions besides solvability are assumed). We use the basic results of M.G. Krein and I.E. Ovcharenko…
We study truncated Bose operators in finite dimensional Hilbert spaces. Spin coherent states for the truncated Bose operators and canonical coherent states for Bose operators are compared. The Lie algebra structure and the spectrum of the…
In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…
Using the SU($N$) representation of the group theory, we derive the general form of the spin swapping operator for the quantum Heisenberg spin-$s$ systems. We further prove that such a spin swapping operator is equal to the spin singlet…
In this brief article we discuss spin polarization operators and spin polarization states of 2+1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the…
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the ` ` tempo operator'', and that…
We present an alternative solution to nonsingular cubic moment problems, using techniques that are expected to be useful for higher-degree truncated moment problems. In particular, we apply the theory of recursively determinate moment…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
We point out the question of ordering momentum operator in the canonical \break quantization of the SU(2) Skyrme Model. Thus, we suggest a new definition for the momentum operator that may solve the infrared problem that appears when we try…
The characterization of quantum polarization of light requires knowledge of all the moments of the Stokes variables, which are appropriately encoded in the multipole expansion of the density matrix. We look into the cumulative distribution…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
When the algebraic variety associated with a truncated moment sequence is finite, solving the moment problem follows a well-defined procedure. However, moment problems involving infinite algebraic varieties are more complex and less…
Employing the covariant language of two-spinors, we find what conditions a curved Lorentzian spacetime must satisfy for existence of a second order symmetry operator for the massive Dirac equation. The conditions are formulated as existence…