Bateman’s gauge and potentials of knotted and linked light fields: the relativistic algebraic approach. (Russian. English summary) Zbl 1371.83048
Summary: We developed the consistent relativistic biquaternionic formalism for Bateman’s general solutions of the free Maxwell
equations which described, in particular, the linked and knotted electric and magnetic Faraday lines of the light beams in
terms of two potentials. The algorithm of constructing the corresponding 4-potential, which does not require the solution of
the Cabibbo and Ferrari zero field conditions, was found. This opens up possibilities for a canonical quantization of
topologically non-trivial light fields and for correct formulation of the problem of a charged quantum particle motion on their
background.
MSC:
83C27 | Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory |
78A40 | Waves and radiation in optics and electromagnetic theory |