Related papers: Relativistic spin operator must be intrinsic
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…
We consider relativistic coherent states for a spin-0 charged particle that satisfy the next additional requirements: (i) the expected values of the standard coordinate and momentum operators are uniquely related to the real and imaginary…
A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived…
A construction of relativistic wave equations on the homogeneous spaces of the Poincar\'{e} group is given for arbitrary spin chains. Parametrizations of the field functions and harmonic analysis on the homogeneous spaces are studied. It is…
We obtain a non-linear generalization of the relativistic diffusion of particles with spin. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic…
The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility…
A Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales.…
The notion of the spin is shown to have two constituents, as exemplified by the spin of the electron. The first one is related to the form of the wave equation and determines the fermion or boson particle type. This implies the spin taking…
The claim that a particle is an irreducible representation of the Poincar\'e group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it…
A spin system on a lattice can usually be modelled at large scales by an effective quantum field theory. A key mathematical result relating the two descriptions is the quantum central limit theorem, which shows that certain spin observables…
We present a systematic procedure to obtain all necessary and sufficient (quantum) constraints on the expectation values for any set of qudit's operators. These constraints---arise form Hermiticity, normalization, and positivity of a…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…
The exact exponential Foldy-Wouthuysen transformation operator applicable for a particle with an arbitrary spin is derived. It can be successfully utilized for verifying any Foldy-Wouthuysen transformation method based on the exponential…
The recently proposed Wigner function for a particle in an infinite lattice [NJP 14, 103009 (2012)] is extended here to include an internal degree of freedom, as spin. The formalism is developed to account for dynamical processes, with or…
Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has…
The work is organized in two main topics. At first we will outline the relation between spin squeezing, quantum metrology and entanglement detection, with a particular focus on the last. We will derive spin squeezing criteria for the…
It is common practice to describe elementary particles by irreducible unitary representations of the Poincar\'e group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincar\'e group.…
The central role played by pseudodifferential operators in relativistic dynamics is very well know. In this work, operators as the Schrodinger one (e.g: square root) are treated from the point of view of the non-local pseudodifferential…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
It is shown that the spin is naturally introduced into classical mechanics if the latter is formulated as dynamics of the phase space density. It is shown that the uncertainty principle, as the amendment in this dynamics, restricts possible…