Publication:
Time-dependent Hilbert spaces, geometric phases, and general covariance in quantum mechanics

dc.contributor.coauthorNA
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorMostafazadeh, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T23:00:36Z
dc.date.issued2004
dc.description.abstractWe investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schrodinger time-evolution identifies the metric with a positive-definite (Ermakov-Lewis) dynamical invariant of the system. Therefore the geometric phases are determined by the metric. We construct a unitary map relating a given time-independent Hilbert space to the time-dependent Hilbert space defined by a positive-definite dynamical invariant. This map defines a transformation that changes the metric of the Hilbert space but leaves the Hamiltonian of the system invariant. We propose to identify this phenomenon with a quantum mechanical analogue of the principle of general covariance of general relativity. We comment on the implications of this principle for geometrically equivalent quantum systems and investigate the underlying symmetry group.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue45082
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.volume320
dc.identifier.doi10.1016/j.physleta.2003.12.008
dc.identifier.eissn1873-2429
dc.identifier.issn0375-9601
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-0346655336
dc.identifier.urihttps://doi.org/10.1016/j.physleta.2003.12.008
dc.identifier.urihttps://hdl.handle.net/20.500.14288/8072
dc.identifier.wos188118600007
dc.keywordsBerry phase
dc.keywordsTransformations
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofPhysics Letters A
dc.subjectPhysics
dc.titleTime-dependent Hilbert spaces, geometric phases, and general covariance in quantum mechanics
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMostafazadeh, Ali
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Mathematics
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