A remark on natural quantum Lagrangians and natural generalized Schroedinger operators in Galilei quantum mechanics

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Authors	JANYŠKA Josef
Year of publication	2001
Type	Article in Periodical
Magazine / Source	Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Natural operator; quantum bundle; quantum connection; quantum Lagrangian; Schroedinger operator
Description	The natural quantum Lagrangians which appear in Galilei general relativistic quantum mechanics are classified by using methods of natural operators. It is proved that all natural quantum Lagrangians are linear combinations (with real coefficients) of the canonical quantum Lagrangian and the product of the scalar curvature of a spacetime vertical connection and the Hermitian product. The classification of all natural generalized Schroedinger operators is given and it is proved that all natural generalized Schroedinger operators can be induced from natural quantum Lagrangians.
Related projects:	Differential geometry of higher order Mathematical structures of algebra and geometry