Spin and the Pauli Equation

2022 ◽  
pp. 356-357
Keyword(s):  
Pauli Equation

scholarly journals PSEUDOCLASSICAL MODEL OF SPINNING PARTICLE WITH ANOMALOUS MAGNETIC MOMENTUM

1993 ◽  
Vol 08 (05) ◽  
pp. 463-468 ◽  
Author(s):  
D.M. GITMAN ◽  
A.V. SAA
Keyword(s):  
Electromagnetic Field ◽  
External Electromagnetic Field ◽  
Invariant Form ◽  
Pauli Equation ◽  
Spinning Particle ◽  
Dirac Quantization

A generalization of the pseudoclassical action of a spinning particle in the presence of an anomalous magnetic momentum is given. The action is written in reparametrization and supergauge invariant form. The Dirac quantization, based on the Hamiltonian analyzes of the model, leads to the Dirac-Pauli equation for a particle with an anomalous magnetic momentum in an external electromagnetic field. Due to the structure of first class constraints in that case, the Dirac quantization demands for consistency to take into account an operator’s ordering problem.

Algebraic structure of Dirac–Pauli equation with account to AMM of neutron in the presence of magnetic field with cylindrical symmetry

2021 ◽  
pp. 2150121
Author(s):  
Masoud Seidi
Keyword(s):  
Magnetic Field ◽  
Lie Algebra ◽  
Algebraic Structure ◽  
Anomalous Magnetic Moment ◽  
Casimir Operator ◽  
Cylindrical Symmetry ◽  
Pauli Equation ◽  
Eigenvalues And Eigenfunctions ◽  
Ladder Operators ◽  
Nu Method

The eigenvalues and eigenfunctions of Dirac–Pauli equation have been obtained for a neutron with anomalous magnetic moment (AMM) in the presence of a strong magnetic field with cylindrical symmetry. In our calculations, the Nikiforov and Uvarov (NU) method has been used. Using the eigenfunctions and construction of the ladder operators, we show that these generators satisfy su(2) Lie algebra and computed the second-order Casimir operator of the lie algebra.

scholarly journals Spectral properties of the equation (∇ + ieA) × u = ±mu

2001 ◽  
Vol 131 (5) ◽  
pp. 1065-1089
Author(s):  
Daniel M. Elton
Keyword(s):  
Spectral Properties ◽  
Time Variable ◽  
Two Dimensional ◽  
Vector Product ◽  
Relativistic Invariance ◽  
Speed Of Light ◽  
Large Parameter ◽  
Real Vector ◽  
Pauli Equation ◽  
Minkowski Metric

We develop a spectral theory for the equation (∇ + ieA) × u = ±mu on Minkowski 3-space (one time variable and two space variables); here, A is a real vector potential and the vector product is defined with respect to the Minkowski metric. This equation was formulated by Elton and Vassiliev, who conjectured that it should have properties similar to those of the two-dimensional Dirac equation. Our equation contains a large parameter c (speed of light), and this motivates the study of the asymptotic behaviour of its spectrum as c → +∞. We show that the essential spectrum of our equation is the same as that of Dirac (theorem 3.1), whereas the discrete spectrum agrees with Dirac to a relative accuracy δλ/mc2 ~ O(c−4) (theorem 3.3). In other words, we show that our equation has the same accuracy as the two-dimensional Pauli equation, its advantage over Pauli being relativistic invariance.

scholarly journals The Pauli equation in scale relativity

2006 ◽  
Vol 39 (40) ◽  
pp. 12565-12585 ◽  
Author(s):  
Marie-Noëlle Célérier ◽  
Laurent Nottale
Keyword(s):  
Pauli Equation ◽  
Scale Relativity

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.

Sign in / Sign up

Export Citation Format

Share Document