NATURALNESS OF THE SPACE OF STATES IN QUANTUM-MECHANICS

Authors
AGUILAR MA SOCOLOVSKY M
Citation
Ma. Aguilar et M. Socolovsky, NATURALNESS OF THE SPACE OF STATES IN QUANTUM-MECHANICS, International journal of theoretical physics, 36(4), 1997, pp. 883-921
Citations number
30
Categorie Soggetti
Physics
Journal title
International journal of theoretical physics → ACNP
ISSN journal
00207748
Volume
36
Issue
4
Year of publication
1997
Pages
883 - 921
Database
ISI
SICI code
0020-7748(1997)36:4<883:NOTSOS>2.0.ZU;2-V
Abstract
We show how certain constructions of quantum mechanics, like monopoles , instantons, and the Schrodinger-von Neumann equation, are related to geometric functors which are representable. We study the differential geometry of the projective bundle associated with an infinite-dimensi onal separable Hilbert space, and we construct a universal connection which is described as a subspace of skew-Hermitian operators. This con nection is responsible for the Berry phase.