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Mini-Workshop: Deformation Quantization: between formal to strict

dc.date.accessioned2019-10-24T15:03:05Z
dc.date.available2019-10-24T15:03:05Z
dc.date.issued2015
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3458
dc.description.abstractThe philosophy of deformation was proposed by Bayen, Flato, Fronsdal, Lichnerowicz, and Sternheimer in the seventies and since then, many developments occurred. Deformation quantization is based on such a philosophy in order to provide a mathematical procedure to pass from classical mechanics to quantum mechanics. Basically, it consists in deforming the pointwise product of functions to get a non-commutative one, which encodes the quantum mechanics behaviour. In formal deformation quantization, the non-commutative product (also said, star product) is given by a formal deformation of the pointwise product, i.e. by a formal power series in the deformation parameter which physically play the role of Planck’s constant $\hbar$. From a physical point of view this is clearly not sufficient to provide a reasonable quantum mechanical description and hence one needs to overcome the formal power series aspects in some way. One option is strict deformation quantization, which produces quantum algebras not just in the space of formal power series but in terms of $C$*-algebras, as suggested by Rieffel, with e.g. a continuous dependence on $\hbar$. There are several other options in between continuous and formal dependence on $\hbar$ like analytic or smooth deformations. The Oberwolfach workshop Deformation quantization: between formal to strict consolidated, continued, and extended these research activities with a focus on the study of the connection between formal and strict deformation quantization in their various flavours and their applications in particular those in quantum physics and non-commutative geometry. It brought together specialists in differential geometry, operator algebras, non-commutative geometry, and quantum field theory with research interests in the mentioned quantization procedures. The aim of the workshop was to develop a coherent viewpoint of the many recent diverse developments in the field and to initiate new lines of research.
dc.titleMini-Workshop: Deformation Quantization: between formal to strict
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWR-2015-11
local.series.idOWR-2015-11
local.subject.msc14
local.subject.msc53
local.sortindex898
local.date-range15 Feb - 21 Feb 2015
local.workshopcode1508c
local.workshoptitleMini-Workshop: Deformation Quantization: between formal to strict
local.organizersPierre Bieliavsky, Louvain-la-Neuve; Chiara Esposito, Würzburg; Ryszard Nest, Copenhagen; Stefan Waldmann, Würzburg
local.report-nameWorkshop Report 2015,11
local.opc-photo-id1508c
local.publishers-doi10.4171/OWR/2015/11
local.ems-referenceBieliavsky Pierre, Esposito Chiara, Nest Ryszard, Waldmann Stefan: Mini-Workshop: Deformation quantization: between formal to strict. Oberwolfach Rep. 12 (2015), 571-595. doi: 10.4171/OWR/2015/11


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