相关论文: Generalized Spin-1/2 Operators and Their Eigenvect…
We propose that the Baxter $Q$-operator for the spin-1/2 XXZ quantum spin chain is given by the $j\to \infty$ limit of the transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. Applying this observation to the open…
We study the general solution of the Yang-Baxter equation with deformed $sl(2)$ symmetry. The universal R operator acting on tensor products of arbitrary representations is obtained in spectral decomposition and in integral forms. The…
The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based…
The general rational solution of the Yang-Baxter equation with the symmetry algebra sl(2) can be represented as the product of the simpler building blocks denoted as R-operators. The R-operators are constructed explicitly and have simple…
We consider a spin coherent states description of a general quantum spin system. It is shown that it is possible to use the spin-1/2 representation to study the general spin-J case. We identify the 1/2 spinor components as the homogeneous…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
Recently it has been shown that the quantum spin-1/2 spin operators can be exactly transformed not only in spinless, but also in spinful canonical Fermi operators in 1D [\cite{JW1}], and 2D [\cite{JW2}] as well. In this paper, using the…
Non-redundant and normalized four-component vector tomographic portrait fully describing the states of spin 1/2 quantum particles was introduced. Dequantizer and quantizer for such portrait were found, and generalization to the case of spin…
Utilizing the previously established general formalism for quantum symmetry reduction in the framework of loop quantum gravity the spectrum of the area operator acting on spherically symmetric states in 4 dimensional pure gravity is…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
This paper constructs a kinematic basis for spin networks with planar or cylindrical symmetry, by exploiting the fact that the basis elements are representations of an O(3) subgroup of O(4). The action of the volume operator on this basis…
We obtain simple formulas for the matrix elements of the resolvent operator (the Green's function) in any finite set of square integrable basis. These formulas are suitable for numerical computations whether the basis elements are…
In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator…
In the present article we calculate the expectation values of of S$_{z}$ and S$^{2}$ operators for spin-1 and spin-3/2 particles by expanding a general wave function which includes all spin values. The results are same as in the stantard…
We continue the discussion of several explicit examples of generalizations in relativistic quantum mechanics. We discussed the generalized spin-1/2 equations for neutrinos and the spin-1 equations for photon. The equations obtained by means…
We present the rigorous derivation of covariant spin operators from a general linear combination of the components of the Pauli-Lubanski vector. It is shown that only two spin operators satisfy the spin algebra and transform properly under…
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…
In quantum mechanics, the connection between the operator algebraic realization and the logical models of measurement of state observables has long been an open question. In the approach that is presented here, we introduce a new…
Although the spin is regarded as a fundamental property of the electron, there is no universally accepted spin operator within the framework of relativistic quantum mechanics. We investigate the properties of different proposals for a…
A description of eigensubspaces of the cosine and sine operators is presented. The spectrum of each of these two operator consists of two eigenvalues (1,\,-1) and their eigensubspaces are infinite--dimensional. There are many possible bases…