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@article{638327,
author = {Janyška, Josef and Modugno, Marco},
article_number = {4},
keywords = {Hermitian vector fields; quantum bundle; special phase functions; Galilei spacetime; Lorentz spacetime},
language = {eng},
issn = {0219-8878},
journal = {International Journal of Geometrical Methods in Modern Physics},
title = {Hermitian vector fields and special phase functions},
url = {http://www.worldscinet.com/ijgmmp/ijgmmp.shtml},
volume = {3},
year = {2006}
}
TY - JOUR
ID - 638327
AU - Janyška, Josef - Modugno, Marco
PY - 2006
TI - Hermitian vector fields and special phase functions
JF - International Journal of Geometrical Methods in Modern Physics
VL - 3
IS - 4
SP - 719-754
EP - 719-754
PB - World Scientific
SN - 02198878
KW - Hermitian vector fields
KW - quantum bundle
KW - special phase functions
KW - Galilei spacetime
KW - Lorentz spacetime
UR - http://www.worldscinet.com/ijgmmp/ijgmmp.shtml
N2 - 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.
ER -
JANYŠKA, Josef and Marco MODUGNO. Hermitian vector fields and special phase functions. \textit{International Journal of Geometrical Methods in Modern Physics}. World Scientific, 2006, vol.~3, No~4, p.~719-754. ISSN~0219-8878.
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