A constructive presentation of rigged Hilbert spaces. (June 2015)
- Record Type:
- Journal Article
- Title:
- A constructive presentation of rigged Hilbert spaces. (June 2015)
- Main Title:
- A constructive presentation of rigged Hilbert spaces
- Authors:
- Celeghini, Enrico
- Abstract:
- Abstract: We construct a rigged Hilbert space for the square integrable functions on the line L2(R) adding to the generators of the Weyl-Heisenberg algebra a new discrete operator, related to the degree of the Hermite polynomials. All together, continuous and discrete operators, constitute the generators of the projective algebra io (2). L 2 (R) and the vector space of the line R are shown to be isomorphic representations of such an algebra and, as both these representations are irreducible, all operators defined on the rigged Hilbert spaces L 2 (R) or R are shown to belong to the universal enveloping algebra of io (2). The procedure can be extended to orthogonal and pseudo-orthogonal spaces of arbitrary dimension by tensorialization. Circumventing all formal problems the paper proposes a kind of toy model, well defined from a mathematical point of view, of rigged Hilbert spaces where, in contrast with the Hilbert spaces, operators with different cardinality are allowed.
- Is Part Of:
- Journal of physics. Number 626(2015)
- Journal:
- Journal of physics
- Issue:
- Number 626(2015)
- Issue Display:
- Volume 626, Issue 626 (2015)
- Year:
- 2015
- Volume:
- 626
- Issue:
- 626
- Issue Sort Value:
- 2015-0626-0626-0000
- Page Start:
- Page End:
- Publication Date:
- 2015-06
- Subjects:
- Physics -- Congresses
530.5 - Journal URLs:
- http://www.iop.org/EJ/journal/1742-6596 ↗
http://ioppublishing.org/ ↗ - DOI:
- 10.1088/1742-6596/626/1/012047 ↗
- Languages:
- English
- ISSNs:
- 1742-6588
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 5036.223000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 7569.xml