Complex geometry and pre-metric electromagnetism

Abstract

The intimate link between complex geometry and the problem of the pre-metric formulation of electromagnetism is explored. In particular, the relationship between 3+1 decompositions of R4 and the decompositions of the vector space of bivectors over R4 into real and imaginary subspaces relative to a choice of complex structure is emphasized. The role of the various scalar products on the space of bivectors that are defined in terms of a volume element on R4 and a complex structure on the space of bivectors that makes it C-linear isomorphic to C3 is discussed in the context of formulation of a theory of electromagnetism in which the Lorentzian metric on spacetime follows as a consequence of the existence of electromagnetic waves, not a prior assumption.

46 pages

References in corpus (2)

• Fresnel analysis of the wave propagation in nonlinear electrodynamics
• Foliated Cobordism and Motion

Cited by in corpus (5)

• Symmetries and pre-metric electromagnetism
• Recent developments in premetric classical electrodynamics
• Generalized Madelung transformations for quantum wave equations I: generalized spherical coordinates for field spaces
• Spinors and pre-metric electromagnetism
• Symmetries of the equations of pre-metric electromagnetism