Related papers: Spin, angular momentum and spin-statistics for a r…
Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are…
We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch…
We explore the possibility that the connection between spin and statistics in quantum physics is of dynamical origin. We suggest that the gravitational field could provide a fully local mechanism for the phase that arises when fermionic and…
This paper was concerned with the spin-momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only…
In a previous paper, we have shown that the classical and quantum relativistic dynamics of the Stueckelberg-Horwitz-Piron [SHP] theory can be embedded in general relativity (GR). We briefly review the SHP theory here, and, in particular,…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
In this paper we propose a unified statistics of Bose-Einstein and Fermi-Dirac statistics by suggesting that every particle can be associated with matter or fundamental forces with certain probability. The main Justification for this…
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 density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
We investigate quantum kinetic theory for a massive fermion system under a rotational field. From the Dirac equation in curved space we derive the complete set of kinetic equations for the spin components of the covariant and equal-time…
A proof is given for the Fourier transform for functions in a quantum mechanical Hilbert space on a non-compact manifold in general relativity. In the (configuration space) Newton-Wigner representation we discuss the spectral decomposition…
In honor of Minkowski's great contribution to Special Relativity, celebrated at this conference, we first review Wigner's theory of the projective irreducible representations of the inhomogeneous Lorentz group. We also sketch those parts of…
We revisit the question of how a definite phase between Bose-Einstein condensates can spontaneously appear under the effect of measurements. We first consider a system that is the juxtaposition of two subsystems in Fock states with high…
A general entangled qubit pair is analyzed in the de Broglie-Bohm formalism corresponding to two spin-1/2 quantum rotors. Several spin-spin correlators of Bohm's hidden variables are analyzed numerically and a detailed comparison with…
Some basic concepts concerning systems of identical particles are discussed in the framework of a realist interpretation, where the wave function is the quantum object and |psi(r)|^2 d^3r is the probability that the wave function causes an…
We study the covariant version of the quark-parton model, in which the general rules of the angular momentum composition are accurately taken into account. We demonstrate how these rules affect the relativistic interplay between the quark…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…