Hermitian vector fields and special phase functions

Details Hermitian vector fields and special phase functions Hermitian vector fields and special phase functions

2005-07-29

arxiv.org/abs/math-ph/0507070v1

Int.J.Geom.Meth.Mod.Phys. 3 (2006) 719-754

Physics

Mathematical Physics

Scientific paper

We start by analysing the Lie algebra of Hermitian vector fields of a Hermitian line bundle. Then, we specify the base space of the above bundle by considering a Galilei, or an Einstein spacetime. Namely, in the first case, we consider, a fibred manifold over absolute time equipped with a spacelike Riemannian metric, a spacetime connection (preserving the time fibring and the spacelike metric) and an electromagnetic field. In the second case, we consider a spacetime equipped with a Lorentzian metric and an electromagnetic field. In both cases, we exhibit a natural Lie algebra of special phase functions and show that the Lie algebra of Hermitian vector fields turns out to be naturally isomorphic to the Lie algebra of special phase functions. Eventually, we compare the Galilei and Einstein cases.

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