Electromagnetic field with constraints and Papapetrou equation

Abstract

It is shown that geometric optical description of electromagnetic wave with account of its polarization in curved space-time can be obtained straightforwardly from the classical variational principle for electromagnetic field. For this end the entire functional space of electromagnetic fields must be reduced to its subspace of locally plane monochromatic waves. We have formulated the constraints under which the entire functional space of electromagnetic fields reduces to its subspace of locally plane monochromatic waves. These constraints introduce variables of another kind which specify a field of local frames associated to the wave and contain some congruence of null-curves. The Lagrangian for constrained electromagnetic field contains variables of two kinds, namely, a congruence of null-curves and the field itself. This yields two kinds of Euler-Lagrange equations. Equations of first kind are trivial due to the constraints imposed. Variation of the curves yields the Papapetrou equations for a classical massless particle with helicity 1.

11 pages, PDF file

References in corpus (1)

• Lagrangian Models of the Particles with Spin: The First Seventy Years

Cited by in corpus (5)

• Motion of Spin 1/2 Massive Particle in a Curved Spacetime
• Motion of a vector particle in a curved space-time. III. Development of techniques of calculation
• Motion of Spin 1/2 Massless Particle in a Curved Spacetime. II. Field Lagrangian Approach
• Variational Principles for Constrained Electromagnetic Field and Papapetrou Equation
• Motion of a Vector Particle in a Curved Space-time. IV. Asymptotical shape of caustic