Related papers: Bases for spin systems and qudits from angular mom…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
The general model of an arbitrary spin massive particle in any dimensional space-time is derived on the basis of Kirillov - Kostant - Souriau approach. Keywords: spinning particles, Poincar\'e group, orbit method, constrained dynamics,…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
The interpretation of quantum mechanics due to Lande' is applied to the connection between wave mechanics and matrix mechanics. The connection between the differential eigenvalue equation and the matrix eigenvalue equation for an operator…
Scattering theory is employed to derive a Landauer-type formula for the spin and the charge currents, through a finite region where spin-orbit interactions are effective. It is shown that the transmission matrix yields the spatial direction…
We study the production of charged scalar particles with well defined angular momentum, in the presence of an external Coulomb field on de Sitter expanding universe. This process of particle production is studied as a perturbative…
We present a brief overview of the current theoretical and experimental progresses in the study of quantum dot-based quantum computing schemes, then focus on the spin-based varieties, which are generally regarded as the most scalable…
This is the third part of our series "Quasiclassical and Quantum Systems of Angular Momentum". In two previous parts we have discussed the methods of group algebras in formulation of quantum mechanics and certain quasiclassical problems.…
In this paper, we propose a method to construct the decay amplitudes in the orbital ($L$) and spin ($S$) coupling scheme for particles with arbitrary spins. For the $1\to 2$ decay with only massive particles involved, the angular dependence…
The quantum theory of rotation angles (S. M. Barnett and D. T. Pegg, Phys. Rev. A, 41, 3427-3425 (1990)) is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the…
The general theoretical ground for the models based on the compact angle coordinates is presented. It is observed that the proper dependence on compact coordinates has to be through the group elements and is achieved most naturally in a…
We show that spin generalization of elliptic Calogero-Moser system, elliptic extension of Gaudin model and their cousins can be treated as a degenerations of Hitchin systems. Applications to the constructions of integrals of motion,…
It is suggested to map the qubits into solid state NMR spin system collective states instead of the states of the individual spin. Such an approach introduces the stable computational basis without any additional actions and allows to…
The representation theory of the quantum group su$_q(2)$ is used to introduce $q$-analogues of the Wigner rotation matrices, spherical functions, and Legendre polynomials. The method amounts to an extension of variable separation from…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
Mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest, since they can be readily implemented in practice. We show that, for a system of qubits, finding such a generator can be cast as…
We use geometric ideas coming from certain classic algebraic constructions to associate, to every classical field theory, a symmetric monoidal double functor from the double category of cobordisms with corners to a certain symmetric…
A concrete representation of the Clifford algebra (for any hyperbolic quadratic space) is given using what are called Suslin matrices. This explicit construction is used to analyze the corresponding Spin groups and the involution and might…
In this paper, we further develop the theory of circles of partition by introducing the notion of complex circles of partition. This work generalizes the classical framework, extending from subsets of the natural numbers as base sets to…
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is…