ELECTROMAGNETIC PARTICLE: MASS, SPIN,

CHARGE,AND MAGNETIC MOMENT

Alexander A. Chernitskii

PARTICLE SOLUTION OF NONLINEARFIELD MODEL AND IDEA OF

INTERACTION

• Particle solution of field model is localized in space and keeps its specific form all the time.

• Motion characteristics for each of two spatially separated particle solutions of nonlinear field model vary because of other particle solution. This is interaction of particles. There is the interaction in nonlinear field models because the sum of solutions is not solution.

NONLINEAR VACUUM (BORN-INFELD)

ELECTRODYNAMICS

General system of equations for electrodynamics outside of singularities:

Nonlinear constitutive relations (of a special kind):

CONSERVATION LAWSfor energy, momentum, and angular

momentum

MASS AND SPIN

• Mass for field inside the volume V is defined as full field energy and spin is defined as full field angular momentum:

• Mass and spin are characteristic of particle solution near the localization region. Static particle solutions of nonlinear electrodynamics can have finite mass and spin for .V

EXAMPLE FOR THE MASSIVE STATIC FIELD CONFIGURATION WITH SPIN: BIDYON

• Two dyon configuration with equal electric and opposite magnetic charges.

• Spin is defined by charges. It does not depend on distance between the dyons.

• Let us take that the spin equals electronic spin and the full electric charge equals electronic charge.

• Then a ratio between electric and magnetic charges of each dyon is fine structure constant.

A. A. Chernitskii. Dyons and Interactions in Nonlinear (Born-Infeld)Electrodynamics. J. High Energy Phys. 1999, No. 12, Paper 10 (1999); http://arxiv.org/abs/hep-th/9911093.

PARTICLE SOLUTION AT INFINITY.CHARGES AND DIPOLE MOMENTS

The field of particle solution at infinity is small. Thus we can use the linear electrodynamic equations for the field at infinity. Expansion on vector spherical functions gives the following approximate expression for this field:

Here and are electric and magnetic monopole moments (charges), and are vectors of electric and magnetic dipole moments.

PARTICLE SOLUTION WITH ADDITIONAL

GIVEN QUASI-CONSTANT WEAK FIELDLet us consider a many-particle field configuration including the particle solution under consideration. In the localization region of this particle we can consider a perturbation method with the following initial approximation:

where are weak quasi-constant field of distant particles.Let us expand the field in Taylor series near the centerof the particle field configuration:

Substitution (*) with (**) into the integral conservation laws gives the classical motion equations for massive charged particle with spin and

(*)

(**)

dipole moments in external field (here in proper inertial coordinate system):

CONCLUSIONS

• The classical motion equations for massive charged particle with spin and dipole moments in external field is obtained in nonlinear electrodynamics from integral conservation laws.

• The mass, spin, charges, and dipole moment naturally appear in motion equations.

• Mass and spin are characteristic for particle solution near the localization region. But charges and dipole moments are characteristic for particle solution at infinity.