Related papers: Proper relativistic position operators in 1+1 and …
We consider the deformation of the Poincar\'e group in 2+1 dimensions into the quantum double of the Lorentz group and construct Lorentz-covariant momentum-space formulations of the irreducible representations describing massive particles…
We present a derivation of a position operator for a massive field with spin $1/2$, expressed in a representation-independent form of the Poincar\'e group. Using the recently derived Lorentz-covariant field spin operator, we obtain a…
Since the discovery a century ago, spin describing the intrinsic angular momentum of massive elementary particles has exposed its nature and significant roles in wide ranges of (relativistic) quantum phenomena and practical applications for…
This work is a natural continuation of our recent study in quantizing relativistic particles. There it was demonstrated that, by applying a consistent quantization scheme to a classical model of a spinless relativistic particle as well as…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
In this paper the relativistic quantum mechanics is considered in the framework of the nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincar{\'e} covariance but (at least formally) distinguishes an inertial…
In this brief article we discuss spin polarization operators and spin polarization states of 2+1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the…
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…
We derive a relativistic-covariant spin operator for massive case directly from space-time symmetry in Minkowski space-time and investigate the physical properties of a derived spin operator. In the derivation we require only two…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…
It is shown that the components of Pryce's spin operator of Dirac's theory are $SU(2)$ generators of a representation carried by the space of Pauli's spinors determining the polarization of the plane wave solutions of Dirac's equation.…
Special-relativistic dynamically-generated elementary-particle mass is represented by a self-adjoint energy operator acting on a rigged Hilbert space (RHS) of functions over the 6-dimensional Euclidean-group manifold. The energy operator is…
Spin degrees of freedom of the Galilean covariant Dirac field in (4+1) dimensions and its nonrelativistic counterpart in (3+1) dimensions are examined. Two standard choices of spin operator, the Galilean covariant and Dirac spin operators,…
We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…
Presented is a quantum computing representation of Dirac particle dynamics. The approach employs an operator splitting method that is an analytically closed-form product decomposition of the unitary evolution operator. This allows the Dirac…
In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of…
The $D$-dimensional $(\beta, \beta')$-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. In the D=3 and $\beta=0$ case, the latter…
We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincar\'e symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
The diffculties of relativistic particle theories formulated my means of canonical quantization, such as Klein-Gordon and Dirac theories, ultimately led theoretical physicists to turn on quantum field theory to model elementary particle…