Poincaré and TCP Invariance in the Determination of Wave Equations for Particles of Arbitrary Spin

1972 ◽  
Vol 13 (7) ◽  
pp. 938-943 ◽  
Author(s):  
M. Seetharaman ◽  
P. M. Mathews
Keyword(s):  
Wave Equations ◽  
Arbitrary Spin

PARADOXICAL KINEMATIC ACAUSALITY IN WEINBERG’S EQUATIONS FOR MASSLESS PARTICLES OF ARBITRARY SPIN

1992 ◽  
Vol 07 (22) ◽  
pp. 1967-1974 ◽  
Author(s):  
D.V. AHLUWALIA ◽  
D.J. ERNST
Keyword(s):  
Wave Equations ◽  
Classical Group ◽  
Arbitrary Spin ◽  
The Other ◽  
Finite Mass ◽  
Massless Particles ◽  
Paradoxical Situation ◽  
Other Hand ◽  
Free Particles

Weinberg’s equations for massless free particles of arbitrary spin are found to have acausal solutions. On the other hand, the m→0 limit of Joos-Weinberg’s finite-mass wave equations satisfied by (j, 0)⊕(0, j) j) covariant spinors are free from all kinematic acausality. This paradoxical situation is resolved and corrected by carefully studying the transition from the classical group theoretical arguments to quantum mechanically interpreted equations.

SPIN DEPENDENCE OF THE AHARONOV—BOHM EFFECT

1991 ◽  
Vol 06 (18) ◽  
pp. 3119-3149 ◽  
Author(s):  
C.R. HAGEN
Keyword(s):  
Wave Equations ◽  
Virial Coefficient ◽  
Arbitrary Spin ◽  
Relativistic Wave Equation ◽  
Spin Dependence ◽  
Polarized Beams ◽  
Bohm Effect ◽  
Spinless Case ◽  
Aharonov Bohm ◽  
Covariant Field

The problem of the proper inclusion of spin in Aharonov—Bohm scattering is considered. It is proposed that this should be accomplished by imposing the requirement that all singularities arising from the presence of spin in the associated wave equations be interpreted as limits of physically realizable flux distributions. This leads to results which confirm the usual cross section in the spinless case but imply nontrivial modifications for the scattering of a polarized spin one-half beam. By applying the technique to a calculation of the virial coefficient for a collection of flux carrying spin one-half particles, some severe obstacles to conventional views of the flux as a parameter which interpolates between bosonic and fermionic statistics are shown to occur. Although similar results for the scattering of arbitrary spin particles obtain in the Galilean limit, it is found that when spin one is considered in the context of a relativistic wave equation the singularity structure is too pathological to yield a consistent interpretation. The exact equivalence of the spin one-half Aharonov-Bohm effect to the Aharonov-Casher effect is also demonstrated and corresponding results for polarized beams are presented. Finally, it is shown that the Aharonov-Bohm effect for arbitrary spin in the Galilean limit is the exact solution in the two-particle sector of a Galilean covariant field theory.

Arbitrary‐Spin Wave Equations and Lorentz Invariance

1971 ◽  
Vol 12 (5) ◽  
pp. 835-840 ◽  
Author(s):  
M. Seetharaman ◽  
J. Jayaraman ◽  
P. M. Mathews
Keyword(s):  
Spin Wave ◽  
Wave Equations ◽  
Lorentz Invariance ◽  
Arbitrary Spin

scholarly journals A GEOMETRIC MODEL OF THE ARBITRARY SPIN MASSIVE PARTICLE

1995 ◽  
Vol 10 (10) ◽  
pp. 1529-1552 ◽  
Author(s):  
S.M. KUZENKO ◽  
S.L. LYAKHOVICH ◽  
A.YU. SEGAL
Keyword(s):  
Wave Equations ◽  
Geometric Model ◽  
Canonical Quantization ◽  
Massive Particle ◽  
Arbitrary Spin ◽  
Dimensional Sphere ◽  
Classical Level ◽  
Gauge Transformations ◽  
Massive Spin ◽  
Casimir Operators

A new model of the relativistic massive particle with arbitrary spin [the (m, s) particle] is suggested. The configuration space of the model is the product of Minkowski space and a two-dimensional sphere: ℳ6=ℝ3, 1×S2. The system describes Zitterbevegung at the classical level. Together with explicitly realized Poincare symmetry, the action functional turns out to be invariant under two types of gauge transformations having their origin in the presence of two Abelian first class constraints in the Hamilton formalism. These constraints correspond to strong conservation for the phase space counterparts of the Casimir operators of the Poincaré group. Canonical quantization of the model leads to equations on the wave functions which prove to be equivalent to the relativistic wave equations for the massive spin s field.

On the determination of Ω − Ω scattering amplitudes from finite volume spectra

2016 ◽  
Vol 31 (35) ◽  
pp. 1650184 ◽  
Author(s):  
Ning Li ◽  
Ya-Jie Wu
Keyword(s):  
Energy Levels ◽  
Arbitrary Spin ◽  
Particle Energy ◽  
Low Energy ◽  
Particle Scattering ◽  
Mechanics Model ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Nonrelativistic Quantum Mechanics

The elastic scattering phase shifts to the two-particle energy levels in a finite cubic box is related by the Lüscher’s formula. In this paper, based on the nonrelativistic quantum mechanics model which is usually assumed to be the low energy scattering case in lattice simulations, we confirmed the generalized Lüscher’s formula for the case of two-particle scattering with arbitrary spin in Ref. 1. In particular, Lüscher’s formula is synthesized for two-spin-3/2-particle scattering, i.e. [Formula: see text] scattering on lattice that may help us study the promising dibaryon states.

A Model for the Fast Determination of Modal Sound Transmission of Large Rectangular Opening

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Jiazhu Li ◽  
Rui Zhang ◽  
Shen Chen ◽  
Can Li ◽  
Jian Chen
Keyword(s):  
Wave Equations ◽  
Three Dimensional ◽  
Sound Transmission ◽  
Computational Effort ◽  
Sound Insulation ◽  
Fast Determination ◽  
High Frequencies ◽  
Higher Order Modes ◽  
Insulation Performance

Abstract The existence of openings affects the sound insulation performance of structures significantly. The determination of sound transmission through large rectangular openings is often time-consuming, because of the large number of modes, especially if there is a need to go to high frequencies. A model is proposed and detailed based on three-dimensional wave equations, the transfer matrix method, and modal superposition. The viscous and thermal boundary layer effects have been concerned; hence, the model accuracy for narrow slits was improved. The computational effort is significantly decreased by neglecting the cross-modal sound transmission. The accuracy of this model is validated by comparing it with the existing model, the measurement, and the acoustic finite element method. The study of sound transmission behavior of higher-order modes is performed. The modal sound transmission is predicted and compared for several modes. The phenomenon that is different from that of the plane wave situation is found and discussed.

The structure of linear relativistic wave equations. I

1950 ◽  
Vol 202 (1069) ◽  
pp. 284-300 ◽  
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Total Spin ◽  
Relativistic Wave Equations ◽  
Relativistic Wave ◽  
Arithmetical Progression ◽  
Physical Requirement ◽  
Complete Determination

The structure of linear relativistic wave equations of the form ( iα µ ∂ µ - X ) ψ = 0 is discussed. In general, such equations describe particles with a spectrum of mass and spin values. It is proved that the physical requirement that all particle states can be unambiguously specified by the momentum, mass, spin and charge, leads to a complete determination of the eigenvalues of the total spin. These must form an arithmetical progression S H , S H — 1, S H — 2, ..., terminating at 0, 1/2 or 1. A coupling diagram is associated with every wave equation and necessary restrictions on the shape of the diagram are worked out. There results a useful reduction in the number of mathematical possibilities.

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