Eigenlösungen der Maxwellgleichungen auf S1 x S3 und konforme Symmetrie, Untersuchungen am U(2)-Programm [article]

Karsten Busse, Martin-Luther Universität, Universitäts- Und Landesbibliothek Sachsen-Anhalt
2018
The solutions of Maxwell's equations on the compact manifold S1 × S3 with pseudoriemannian signature are determined. Their form form is chosen with respect to the Cartan subalgebra of the conformal group SU(2,2) to be eigensolutions of the generating operators. Topologically the Cartan subalgebra corresponds to a (maximal) torus, created by the S1 direction and the two Heegaard tori of the 3 sphere. The components of the solutions are represented by contiguous Riemann's P-functions, like the
more » ... ctions, like the known solutions of the Klein-Gordon equation are represented too. In two special cases some interesting results occur. For a scalar field with discrete mass spectrum every fourth mass value (m0=2 Mod 4) is forbidden. Harmonic potentials of Maxwell's equations with restriction on the maximal torus occur in three classes of solutions with two free quantum numbers (eigenvalues) each and a fourth class with fixed quantum numbers. As the manifolds S1 × S3 and M4 are conformal equivalent ones the solutions may be interpreted in a conformal field theory.
doi:10.25673/2609 fatcat:ewdpuajijnfqzjiverub46hvny