Matches in SemOpenAlex for { <https://semopenalex.org/work/W2293314133> ?p ?o ?g. }
Showing items 1 to 58 of
58
with 100 items per page.
- W2293314133 abstract "Acting within the framework of the geometric quantum mechanics, we give a Jacobi field interpretation of the quantum mechanical uncertainty. Then a link with elliptic curves via the classical integrability of Schrodinger dynamics and the cross ratio interpretation of quantum probabilities is established. Furthermore a geometrical construction of all special unitary representations of the three-strand braid group on the quantum onequbit space is provided. 1. Integrability in Quantum Mechanics 1.1. Geometry of Quantum Mechanics We start this paper by briefly reviewing geometric quantum mechanics and, in particular, the completely integrable structure of Schrodinger dynamics in finite dimensional quantum space (cf. [1–4, 6, 15]). Throughout the paper we assume ~ = 1. Let V be a complex Hilbert space of dimension n+1 with a scalar product 〈·|·〉 which is linear in the second variable. We shall freely use the Dirac notation. The space of pure states in quantum mechanics is the projective space associated to V , denoted by P(V ), of complex dimension n, whose points are the rays [v] (directions) pertaining to nonzero vectors |v〉. Considering the actions of the unitary group U(V ) associated to (V, 〈·|·〉) and its Lie algebra u(V ), consisting of all skew-hermitian endomorphisms of V (the quantum observables, and with a slight abuse of language), the projective space P(V ) becomes a U(V )-homogeneous Kahler manifold. Furthermore we can identify a point in P(V ) with the projection operator" @default.
- W2293314133 created "2016-06-24" @default.
- W2293314133 creator A5022260040 @default.
- W2293314133 date "2012-01-01" @default.
- W2293314133 modified "2023-09-26" @default.
- W2293314133 title "On Uncertainty, Braiding and Jacobi Fields in Geometric Quantum Mechanics" @default.
- W2293314133 doi "https://doi.org/10.7546/giq-8-2007-127-134" @default.
- W2293314133 hasPublicationYear "2012" @default.
- W2293314133 type Work @default.
- W2293314133 sameAs 2293314133 @default.
- W2293314133 citedByCount "0" @default.
- W2293314133 crossrefType "report" @default.
- W2293314133 hasAuthorship W2293314133A5022260040 @default.
- W2293314133 hasConcept C11255438 @default.
- W2293314133 hasConcept C121332964 @default.
- W2293314133 hasConcept C15184713 @default.
- W2293314133 hasConcept C15706264 @default.
- W2293314133 hasConcept C186123792 @default.
- W2293314133 hasConcept C33923547 @default.
- W2293314133 hasConcept C43682372 @default.
- W2293314133 hasConcept C62520636 @default.
- W2293314133 hasConcept C84114770 @default.
- W2293314133 hasConceptScore W2293314133C11255438 @default.
- W2293314133 hasConceptScore W2293314133C121332964 @default.
- W2293314133 hasConceptScore W2293314133C15184713 @default.
- W2293314133 hasConceptScore W2293314133C15706264 @default.
- W2293314133 hasConceptScore W2293314133C186123792 @default.
- W2293314133 hasConceptScore W2293314133C33923547 @default.
- W2293314133 hasConceptScore W2293314133C43682372 @default.
- W2293314133 hasConceptScore W2293314133C62520636 @default.
- W2293314133 hasConceptScore W2293314133C84114770 @default.
- W2293314133 hasLocation W22933141331 @default.
- W2293314133 hasOpenAccess W2293314133 @default.
- W2293314133 hasPrimaryLocation W22933141331 @default.
- W2293314133 hasRelatedWork W2035318096 @default.
- W2293314133 hasRelatedWork W2036255255 @default.
- W2293314133 hasRelatedWork W2041565758 @default.
- W2293314133 hasRelatedWork W2043744949 @default.
- W2293314133 hasRelatedWork W2067210264 @default.
- W2293314133 hasRelatedWork W2074781741 @default.
- W2293314133 hasRelatedWork W2077033164 @default.
- W2293314133 hasRelatedWork W2080009116 @default.
- W2293314133 hasRelatedWork W2136329591 @default.
- W2293314133 hasRelatedWork W2245265755 @default.
- W2293314133 hasRelatedWork W2273112994 @default.
- W2293314133 hasRelatedWork W2500304526 @default.
- W2293314133 hasRelatedWork W2734049981 @default.
- W2293314133 hasRelatedWork W3101671216 @default.
- W2293314133 hasRelatedWork W3101807421 @default.
- W2293314133 hasRelatedWork W3105875117 @default.
- W2293314133 hasRelatedWork W3106006873 @default.
- W2293314133 hasRelatedWork W31434249 @default.
- W2293314133 hasRelatedWork W365999814 @default.
- W2293314133 hasRelatedWork W605771338 @default.
- W2293314133 isParatext "false" @default.
- W2293314133 isRetracted "false" @default.
- W2293314133 magId "2293314133" @default.
- W2293314133 workType "report" @default.