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Article: Geometric quantization, parallel transport and the fourier transform

TitleGeometric quantization, parallel transport and the fourier transform
Authors
Issue Date2006
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00220/index.htm
Citation
Communications In Mathematical Physics, 2006, v. 266 n. 3, p. 577-594 How to Cite?
AbstractIn quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle H over the space ∂ of compatible complex structures on a symplectic vector space. This bundle is equipped with a projectively flat connection. We show that parallel transport along a geodesic in the bundle H → J is a rescaled orthogonal projection or Bogoliubov transformation. We then construct the kernel for the integral parallel transport operator. Finally, by extending geodesics to the boundary (for which the metaplectic correction is essential), we obtain the Segal-Bargmann and Fourier transforms as parallel transport in suitable limits.
Persistent Identifierhttp://hdl.handle.net/10722/75229
ISSN
2015 Impact Factor: 2.375
2015 SCImago Journal Rankings: 1.760
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorKirwin, WDen_HK
dc.contributor.authorWu, Sen_HK
dc.date.accessioned2010-09-06T07:09:10Z-
dc.date.available2010-09-06T07:09:10Z-
dc.date.issued2006en_HK
dc.identifier.citationCommunications In Mathematical Physics, 2006, v. 266 n. 3, p. 577-594en_HK
dc.identifier.issn0010-3616en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75229-
dc.description.abstractIn quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle H over the space ∂ of compatible complex structures on a symplectic vector space. This bundle is equipped with a projectively flat connection. We show that parallel transport along a geodesic in the bundle H → J is a rescaled orthogonal projection or Bogoliubov transformation. We then construct the kernel for the integral parallel transport operator. Finally, by extending geodesics to the boundary (for which the metaplectic correction is essential), we obtain the Segal-Bargmann and Fourier transforms as parallel transport in suitable limits.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00220/index.htmen_HK
dc.relation.ispartofCommunications in Mathematical Physicsen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsThe original publication is available at www.springerlink.com-
dc.titleGeometric quantization, parallel transport and the fourier transformen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0010-3616&volume=266 No3&spage=577&epage=594&date=2006&atitle=Geometric+quantization,+parallel+transport+and+the+Fourier+transformen_HK
dc.identifier.emailWu, S:swu@maths.hku.hken_HK
dc.identifier.authorityWu, S=rp00814en_HK
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1007/s00220-006-0043-zen_HK
dc.identifier.scopuseid_2-s2.0-33747497093en_HK
dc.identifier.hkuros128448en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33747497093&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume266en_HK
dc.identifier.issue3en_HK
dc.identifier.spage577en_HK
dc.identifier.epage594en_HK
dc.identifier.eissn1432-0916-
dc.identifier.isiWOS:000239817600001-
dc.publisher.placeGermanyen_HK
dc.identifier.scopusauthoridKirwin, WD=14071696700en_HK
dc.identifier.scopusauthoridWu, S=15830510400en_HK

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