Quantum operators and Hermitian vector fields
| Authors | |
|---|---|
| Year of publication | 2006 |
| Type | Article in Proceedings |
| Conference | DIFFERENTIAL GEOMETRY AND PHYSICS |
| MU Faculty or unit | |
| 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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