ApproximateSU3and Its Nonrelativistic Limit

1967 ◽  
Vol 158 (5) ◽  
pp. 1560-1565 ◽  
Author(s):  
O. Fleischman ◽  
P. Roman
Keyword(s):  
Nonrelativistic Limit

scholarly journals ELECTROMAGNETIC INTERACTION OF ANYONS IN NONRELATIVISTIC QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (06) ◽  
pp. 953-967 ◽  
Author(s):  
J. L. CORTÉS ◽  
J. GAMBOA ◽  
L. VELÁZQUEZ
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Interaction ◽  
Magnetic Coupling ◽  
Nonrelativistic Limit ◽  
Quantum Field ◽  
Nonrelativistic Quantum ◽  
Statistical Field ◽  
Mechanical Formulation ◽  
Dynamical Spin ◽  
Chern Simons

The nonrelativistic quantum-field-theoretic Lagrangian which describes an anyon system in the presence of an electromagnetic field is identified. A nonminimal magnetic coupling to the Chern–Simons statistical field as well as to the electromagnetic field together with a direct coupling between both fields are the nontrivial ingredients of the Lagrangian obtained from the nonrelativistic limit of the fermionic relativistic formulation. The results, an electromagnetic gyromagnetic ratio 2 for any spin together with a nontrivial dynamical spin-dependent contact interaction between anyons as well as the spin dependence of the electromagnetic effective action, agree with the quantum-mechanical formulation.

scholarly journals Simple prescription for computing the nonrelativistic interparticle potential energy related to dual models

2016 ◽  
Vol 31 (12) ◽  
pp. 1650070 ◽  
Author(s):  
G. B. de Gracia ◽  
G. P. de Brito
Keyword(s):  
Vector Field ◽  
Potential Energy ◽  
Nonrelativistic Limit ◽  
External Current ◽  
Interparticle Potential ◽  
Higher Derivative ◽  
Higher Derivatives ◽  
Rank 2 ◽  
Electromagnetic Models ◽  
Dual Models

Following a procedure recently utilized by Accioly et al. to obtain the D-dimensional interparticle potential energy for electromagnetic models in the nonrelativistic limit, and relaxing the condition assumed by the authors concerning the conservation of the external current, the prescription found out by them is generalized so that dual models can also be contemplated. Specific models in which the interaction is mediated by a spin-0 particle described first by a vector field and then by a higher-derivative vector field, are analyzed. Systems mediated by spin-1 particles described, respectively, by symmetric rank-2 tensors, symmetric rank-2 tensors augmented by higher derivatives and antisymmetric rank-2 tensors, are considered as well.

scholarly journals ANY l-STATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE WOODS–SAXON POTENTIAL

2010 ◽  
Vol 19 (07) ◽  
pp. 1463-1475 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
S. V. BADALOV
Keyword(s):  
State Energy ◽  
Gordon Equation ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Saxon Potential ◽  
Bound State Energy ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Pekeris Approximation ◽  
Klein Gordon Equation

The radial part of the Klein–Gordon equation for the Woods–Saxon potential is solved. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for any l-states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained on the various values of the quantum numbers n and l. The nonrelativistic limit of the bound state energy spectrum was also found.

scholarly journals SPINNING PARTICLES ON SPACELIKE HYPERSURFACES AND THEIR REST FRAME DESCRIPTION

1999 ◽  
Vol 14 (09) ◽  
pp. 1429-1484 ◽  
Author(s):  
FRANCESCO BIGAZZI ◽  
LUCA LUSANNA
Keyword(s):  
Spin Structure ◽  
Rest Frame ◽  
Negative Energy ◽  
Nonrelativistic Limit ◽  
Critical Discussion ◽  
Positive Energy ◽  
Spinning Particle ◽  
Spinning Particles ◽  
Spacelike Hypersurfaces ◽  
Energy Formula

A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. It is the pseudoclassical basis of the positive energy [Formula: see text] [or negative energy [Formula: see text]] part of the [Formula: see text] solutions of the Dirac equation. The study of the isolated system of N such spinning charged particles plus the electromagnetic field leads to their description in the rest frame Wigner-covariant instant form of dynamics on the Wigner hyperplanes orthogonal to the total four-momentum of the isolated system (when it is timelike). We find that on such hyperplanes these spinning particles have a nonminimal coupling only of the type "spin–magnetic field," like the nonrelativistic Pauli particles to which they tend in the nonrelativistic limit. The Lienard–Wiechert potentials associated with these charged spinning particles are found. Then, a comment is made on how to quantize the spinning particles respecting their fibered structure describing the spin structure.

Bifurcation and Chaos in a Periodically Driven Quartic Oscillator at Relativistic Energies

1997 ◽  
Vol 07 (04) ◽  
pp. 945-949
Author(s):  
Sang Wook Kim ◽  
Hai-Woong Lee
Keyword(s):  
Chaotic Behavior ◽  
Relativistic Effects ◽  
Critical Value ◽  
Nonrelativistic Limit ◽  
Classical Dynamics ◽  
Bifurcation Diagrams ◽  
Bifurcation And Chaos ◽  
Force Amplitude ◽  
Regular Motion ◽  
Periodically Driven

The classical dynamics of a damped quartic oscillator driven by a sinusoidal force is investigated, with particular attention to the effects that arise when the motion of the oscillator becomes relativistic. Bifurcation diagrams constructed numerically indicate that, as relativistic effects become strong, chaotic behavior exhibited by the oscillator in the nonrelativistic limit at large force amplitude is replaced by a period-1 regular motion. At relativistic energies, therefore, a transition from chaos to a regular motion occurs as the force amplitude is increased beyond a critical value. The transition is seen to occur abruptly with a slight increase of the force amplitude from below to above the critical value. The sudden destruction of the chaotic attractor is probably triggered by the mechanism of crisis.

scholarly journals ON THE ASYMPTOTIC ANALYSIS OF THE DIRAC–MAXWELL SYSTEM IN THE NONRELATIVISTIC LIMIT

2005 ◽  
Vol 02 (01) ◽  
pp. 129-182 ◽  
Author(s):  
PHILIPPE BECHOUCHE ◽  
NORBERT J. MAUSER ◽  
SIGMUND SELBERG
Keyword(s):  
Convergence Result ◽  
Nonrelativistic Limit ◽  
Dirac Spinor ◽  
Maxwell System ◽  
Poisson System ◽  
Pauli Equation ◽  
Existence Time ◽  
Self Consistent Field ◽  
Klein Gordon ◽  
Well Posed

We study the behavior of solutions of the Dirac–Maxwell system (DM) in the nonrelativistic limit c → ∞, where c is the speed of light. DM is a nonlinear system of PDEs obtained by coupling the Dirac equation for a 4-spinor to the Maxwell equations for the self-consistent field created by the moving charge of the spinor. The limit c → ∞, sometimes also called post-Newtonian, yields a Schrödinger–Poisson system, where the spin and magnetic field no longer appear. We prove that DM is locally well-posed for H1 data (for fixed c), and that as c → ∞ the existence time grows at least as fast as log(c), provided the data are uniformly bounded in H1. Moreover, if the datum for the Dirac spinor converges in H1, then the solution of DM converges, modulo a phase correction, in C([0,T];H1) to a solution of a Schrödinger–Poisson system. Our results also apply to a mixed state formulation of DM, and give also a convergence result for the Pauli equation as the "semi-nonrelativistic" limit. The proof relies on modifications of the bilinear null form estimates of Klainerman and Machedon, and extends our previous work on the nonrelativistic limit of the Klein–Gordon–Maxwell system.

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