On complex structures in physics

Details On complex structures in physics On complex structures in physics

1998-09-24

arxiv.org/abs/math-ph/9809022v1

Physics

Mathematical Physics

20 pages, 1 figure, LaTeX

Scientific paper

Complex numbers enter fundamental physics in at least two rather distinct ways. They are needed in quantum theories to make linear differential operators into Hermitian observables. Complex structures appear also, through Hodge duality, in vector and spinor spaces associated with space-time. This paper reviews some of these notions. Charge conjugation in multidimensional geometries and the appearance of Cauchy-Riemann structures on Lorentz manifolds with a congruence of null geodesics without shear are presented in considerable detail.

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