Related papers: Remarks on the Configuration Space Approach to Spi…
Operators that are associated with several important quantities, like angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into…
Starting with the first-order singular Lagrangian, the canonical structure in the noncommutative quantum mechanics with the noncommutativities both of coordinates and momenta is investgated. Using the projection operator method (POM) for…
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized…
An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent…
Elementary particles are found in two different situations: (i) bound to metastable states of matter, for which angular momentum is quantized, and (ii) free, for which, due to their high energy-momentum and leaving aside inner a.m. or spin,…
The diagonalization of the metrical and canonical Hamilton operators of a scalar field with an arbitrary coupling, with a curvature in N-dimensional homogeneous isotropic space is considered in this paper. The energy spectrum of the…
The approach to quantum mechanics which we have used to derive the matrix treatment of spin from first principles is now employed to treat systems of compounded angular momentum. A general treatment is first given, which is then applied to…
The quantum mechanical operator for angular momentum is transformed from the real plane into the complex plane. In doing so, the Cauchy-Riemann (C-R) equations are interpreted as constraint conditions defining two distinct domains where…
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…
The measurement of a spin-$\half$ is modeled by coupling it to an apparatus, that consists of an Ising magnetic dot coupled to a phonon bath. Features of quantum measurements are derived from the dynamical solution of the measurement,…
The traditional Standard Quantum Mechanics (SQM) theory is unable to solve the Spin-s problem, i.e., to justify the utterly important "Pauli Exclusion Principle". A complete and straightforward solution of the Spin-Statistics problem is…
We determine the complete set of generalized spin squeezing inequalities, given in terms of the collective angular momentum components, for particles with an arbitrary spin. They can be used for the experimental detection of entanglement in…
Two vector operators aimed at shifting angular momentum quantum number l in spherical harmonics |lm>, primarily proposed by Prof. X. L. Ka in 2001, are further studied. For a given magnetic quantum number m, specific states |lm> in…
We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and…
Both the topics of entanglement and particle statistics have aroused enormous research interest since the advent of quantum mechanics. Using two pairs of entangled particles we show that indistinguishability enforces a transfer of…
The paper studies spin-orbit interaction (i.e. the effect the spin has on the particle's trajectory in a magnetic field) as a model of quantum computation. The two-level spin quantum system is examined using the stochastic mechanics…
Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…
A general method to construct free quantum fields for massive particles of arbitrary definite spin in a canonical Hamiltonian framework is presented. The main idea of the method is as follows: a multicomponent Klein-Gordon field that…
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 notion of incompressible momentum observables is introduced. It is shown that when the metric in a manifold has a certain form, a set of canonically conjugate variables Xk and Pk in which Pk are incompressible, can be constructed. Based…