Complex geometry and pre-metric electromagnetism

Details Complex geometry and pre-metric electromagnetism Complex geometry and pre-metric electromagnetism

2004-12-10

arxiv.org/abs/gr-qc/0412048v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

46 pages

Scientific paper

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.

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