Magnetic moment of a charged quantum particle as a relativistic distribution of matter

Alexander J. Silenko

V. V. Dodonov, Matheus B. Horovits

Gordon Baym

The Pauli spin matrices have many useful properties. The spin of a particle is a degree of freedom additional to the spatial degrees of freedom. It is independent of the spatial degrees of freedom in the sense that one can simultaneously specify the spin state and the spatial state of a particle. Non-relativistically one must use more indirect methods of observing the spin. Classically, a spinning distribution of charge will have a magnetic moment; quantum mechanical spinning particles also have magnetic moments associated with their spins, and one tries to observe these magnetic moments in experiments. Spins in magnetic fields have very interesting dynamical properties. The right side is just the torque exerted by a magnetic field on a magnetic moment. This equation says in operator language that the rate of change of the spin angular momentum is the applied torque.

Robert J. Gould

In a purely nonrelativistic formulation, a Hamiltonian is obtained for the description of states of a charged particle with spin, interacting with an external electromagnetic field. For the specific cases of spin-1/2 and spin-1, the simplest choices for the Hamiltonian functions lead to a value for the (lowest order) intrinsic magnetic moment equal to the Bohr magneton in both cases. This is the same as is obtained in treatments that start from a relativistic formulation, as in the Dirac theory. The nonrelativistic and relativistic formulations both employ the ‘‘minimal coupling principle,’’ but the resulting Hamiltonians with couplings are, for very general considerations, not completely determined. However, the corresponding ambiguity that occurs in the nonrelativistic theory is also present in the relativistic formulation. The simpler nonrelativistic theory is more transparent in exhibiting these features of the problem and dispels the notion that spin (and the associated magnetic moment) require relativistic formulations for a proper understanding.

V V Semenov

It is shown that a relativistic spin-1/2 neutral particle with an anomalous magnetic moment moving in an x-y plane in a two-dimensional electrostatic field: E=(E x ( x , y ), E y ( x , y ), O) has (N-1)-fold degeneracy of the ground state. The degree of degeneracy of the ground state is defined by the value of the anomalous magnetic moment and a linear charge density of the filament creating this electrostatic field.

Eliade N. Stefanescu