title: On the space of Schwartz operators in the symmetric Fock space and its dual
metadata.name: dc.contributor.author
metadata.value: Amosov, Grigori G.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Baitenov, Egor L.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-07-07T20:59:11Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-07-07T20:59:11Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Amosov G.G., Baitenov E. L. On the space of Schwartz operators in the symmetric Fock space and its dual. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 2, pp. 193–200.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.201
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/37099
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A long-standing problem that arises when constructing the mathematical apparatus of
  quantum mechanics is the need to work with unbounded operators. Since the space of nuclear
  operators is preconjugate for the algebra of all bounded operators, we can consider
  the states of a quantum system as nuclear operators, and consider bounded operators as
  observables. In this case, taking the trace for the product of a nuclear operator (a quantum
  state) and a bounded operator (a quantum observable) gives the average value of a quantum
  observable in a fixed state. The existence of such an average for unbounded operators
  is not guaranteed. If we want to define a space of observables that includes such naturally
  occurring unbounded operators as the position and momentum operators, for which average
  values are always determined, we should consider a space of states smaller than all
  nuclear operators. Recently, this approach has been mathematically correct implemented in
  the Hilbert space H = L2(RN). The so-called space of Schwarz operators, equipped with a
  system of semi-norms and being a Frechet space, was chosen as the space of states. Schwarz
  operators appeared to be integral operators whose kernels are functions belonging to the
  usual Schwarz space. The dual space to the space of Schwarz operators should be considered
  as the space of quantum observables and it really includes such standard observables
  as polynomials from the products of the position and momentum operators. In the present
  work we transfer this approach to the symmetric Fock space H = F(H) over an infinite
  dimensional separable Hilbert space H. We introduce the space of Schwartz operators in
  F(H) over an infinite dimensional separable space H and investigate which of the standard
  operators of quantum white noise belong to the space dual to the space of Schwartz operators.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 9 (67); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: the space of Schwartz operators
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the symmetric Fock space
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quantum white noice
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On the space of Schwartz operators in the symmetric Fock space and its dual
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 193-200.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/37099/1/193-200.pdf
resources.format: Adobe PDF
resources.size: 300,12 kB