Related papers: Rotations and e, $\nu$ Propagators, Part II
On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincar\'{e} group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the…
Mass is proportional to phase gain per unit time; for e, $\pi$, and p the quantum frequencies are 0.124, 32.6, and 227 Zhz, respectively. By explaining how these particles acquire phase at different rates, we explain why these particles…
In this paper we extend our previous result on the description of the partcle motion in a generalized Heisenberg picture to a relativistic fermion. The operators of the Lorentz algebra in this picture may be regarded as field operators. In…
We discuss the numerical solution of the Schr\"odinger equation with a time-dependent Hamilton operator using commutator-free time-propagators. These propagators are constructed as products of exponentials of simple weighted sums of the…
In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for two-dimensional quantum integrable models, especially for the lattice versions of the nonlinear Schrodinger and sine-Gordon…
We elaborate on the traceless and transverse spin projectors in four-dimensional de Sitter and anti-de Sitter spaces. The poles of these projectors are shown to correspond to partially massless fields. We also obtain a factorisation of the…
Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators.…
Polymer Quantum Mechanics is based on some of the techniques used in the loop quantization of gravity that are adapted to describe systems possessing a finite number of degrees of freedom. It has been used in two ways: on one hand it has…
Massive spin 1/2 particles require 2-spinors for rotations, 4-spinors for rotations and boosts with parity. Including translations requires 8-spinors. Adapting 4-spinor field theory to 8-spinor fields with translation symmetry is discussed…
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…
The di-fermion angular distribution observed in decays of inclusively produced vector particles is characterized by two frame-independent observables, reflecting the average spin-alignment of the produced particle and the magnitude of…
The quantum mechanical time-evolution is studied for a particle under the influence of an explicitly time-dependent rotating potential. We discuss the existence of the propagator and we show that in the limit of rapid rotation it converges…
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works.…
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 article presents four identities containing the spatio-temporal differential operator also known as four-divergence. These equations are used to prove the invariance of wave equation under orthogonal paravector transformations.…
The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher…
We write down an explicit projection that maps any given 4-spinor to a point in 3+1 spacetime while commuting with the Lorentz action. This suggests that a Lorentz invariant theory - including spacetime itself - has a more natural…
We apply the exponential operator method to derive the propagator for a fermion immersed within a rigidly rotating environment with cylindrical geometry. Given that the rotation axis provides a preferred direction, Lorentz symmetry is lost…
The propagator of a spinless particle is calculated from the quantum mechanical path integral formalism in static curved spacetimes endowed with event-horizons. A toy model, the Gui spacetime, and the 2D and 4D Schwarzschild black holes are…
We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical…