Nonlinear magnetic response of the magnetized vacuum to applied electric field

We find first nonlinear correction to the field, produced by a static charge at rest in a background constant magnetic field. It is quadratic in the charge and purely magnetic. The third-rank polarization tensor - the nonlinear response function - is written within the local approximation of the effective action in an otherwise model- and approximation-independent way within any P-invariant nonlinear electrodynamics, QED included.Comment: 11 pages without figures or tables. Numerical coefficients and some signs in Version I corrected, three new references and two equations adde

When electric charge becomes also magnetic

In nonlinear electrodynamics, QED included, we find a static solution to the field equations with an electric charge as its source, which is comprised of homogeneous parallel magnetic and electric fields, and a radial spherically-nonsymmetric long-range magnetic field, whose magnetic charge is proportional to the electric charge and also depends on the homogeneous component of the solution.Comment: Four pages, no figure

Path integral and pseudoclassical action for spinning particle in external electromagnetic and torsion fields

Starting from the Dirac equation in external electromagnetic and torsion fields we derive a path integral representation for the corresponding propagator. An effective action, which appears in the representation, is interpreted as a pseudoclassical action for a spinning particle. It is just a generalization of Berezin-Marinov action to the background under consideration. Pseudoclassical equations of motion in the nonrelativistic limit reproduce exactly the classical limit of the Pauli quantum mechanics in the same case. Quantization of the action appears to be nontrivial due to an ordering problem, which needs to be solved to construct operators of first-class constraints, and to select the physical sector. Finally the quantization reproduces the Dirac equation in the given background and, thus, justifies the interpretation of the action.Comment: 18 pages, LaTeX. Small modifications, some references added. To be published in International Journal of Modern Physics

New Exact Solutions Describing Quantum Asymmetric Top

In this work, using the noncommutative integration method of linear differential equations, we obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown that the noncommutative reduction of the Schrodinger equation leads to the Lame equation. The resulting set of solutions is determined by the Lame polynomials in a complex parameter, which is related to the geometry of the orbits of the coadjoint representation of the rotation group. The spectrum of an asymmetric top is obtained from the condition that the solutions are invariant with respect to a special irreducible λ-representation of the rotation group

New Exact Solutions Describing Quantum Asymmetric Top

In this work, using the noncommutative integration method of linear differential equations, we obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown that the noncommutative reduction of the Schrodinger equation leads to the Lame equation. The resulting set of solutions is determined by the Lame polynomials in a complex parameter, which is related to the geometry of the orbits of the coadjoint representation of the rotation group. The spectrum of an asymmetric top is obtained from the condition that the solutions are invariant with respect to a special irreducible λ-representation of the rotation group.</jats:p