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Conformal Inversion and Maxwell Field Invariants in Four- and Six-dimensional Spacetimes

  • Steven DuplijEmail author
  • Gerald A. Goldin
  • Vladimir Shtelen
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

Conformally compactified (3+1)-dimensional Minkowski spacetime may be identified with the projective light cone in (4+2)-dimensional spacetime. In the latter spacetime the special conformal group acts via rotations and boosts, and conformal inversion acts via reflection in a single coordinate. Hexaspherical coordinates facilitate dimensional reduction of Maxwell electromagnetic field strength tensors to (3+1) from (4+2) dimensions. Here we focus on the operation of conformal inversion in different coordinatizations, and write some useful equations. We then write a conformal invariant and a pseudo-invariant in terms of field strengths; the pseudo-invariant in (4 + 2) dimensions takes a new form. Our results advance the study of general nonlinear conformal-invariant electrodynamics based on nonlinear constitutive equations.

Keywords

Conformal symmetry electromagnetism nonlinear constitutive equations 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Steven Duplij
    • 1
    Email author
  • Gerald A. Goldin
    • 2
  • Vladimir Shtelen
    • 3
  1. 1.Dept. of Physics and TechnologyV.N. Karazin Kharkov National UniversityKharkovUkraine
  2. 2.Departments of Mathematics and PhysicsRutgers UniversityPiscatawayUSA
  3. 3.Department of MathematicsRutgers UniversityPiscatawayUSA

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