On the geometry of quantum states

Journal Article · Tue Feb 20 04:00:00 EST 1996 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.49720· OSTI ID:21156234

Aguilar, M A; Socolovsky, M ^[1]

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1. Instituto de Matematicas, Instituto de Ciencias Nucleares, UNAM, Cd. Universitaria, 04510 Mexico, D.F. (Mexico)

Using category theory we show that basic elements of quantum theory, like complexifications, Clifford algebras and projective spaces, appear naturally as universal objects of functors. We give the homotopy equivalence between the U(1)-classifying bundle in topology and the projective bundle associated with a separable Hilbert space.

• OSTI ID: 21156234
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 359; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CLIFFORD ALGEBRA
GEOMETRY
HILBERT SPACE
QUANTUM FIELD THEORY
TOPOLOGY
U-1 GROUPS