Quantum operators and Hermitian vector fields

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Authors

JANYŠKA Josef MODUGNO Marco

Year of publication 2006
Type Article in Proceedings
Conference DIFFERENTIAL GEOMETRY AND PHYSICS
MU Faculty or unit

Faculty of Science

Citation
Web http://www.worldscibooks.com/mathematics/6305.html
Field General mathematics
Keywords Hermitian vector fields; quantum bundle; special phase functions; Galilei spacetime; Lorentz spacetime
Description We classify the Lie algebra of Hermitian vector fields of a Hermitian line bundle, by means of a generic Hermitian connection. Then, we specify the base space of the above Hermitian bundle by considering a Galilei, or an Einstein spacetime. In these cases, the geometric structure of the base space yields a distinguished choice for the Hermitian connection. Then, we can prove that the Lie algebra of Hermitian vector fields turns out to be naturally isomorphic to the Lie algebra of special phase functions.
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