Details
| Original language | English |
|---|---|
| Title of host publication | Semigroups, Algebras and Operator Theory |
| Subtitle of host publication | ICSAOT 2022 |
| Editors | A.A. Ambily, V.B. Kiran Kumar |
| Publisher | Springer |
| Pages | 195-228 |
| Number of pages | 34 |
| ISBN (print) | 9789819963485 |
| Publication status | Published - 1 Feb 2024 |
| Event | International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022 - Cochin, India Duration: 28 Mar 2022 → 31 Mar 2022 |
Publication series
| Name | Springer Proceedings in Mathematics and Statistics |
|---|---|
| Volume | 436 |
| ISSN (Print) | 2194-1009 |
| ISSN (electronic) | 2194-1017 |
Abstract
The resolvent algebra.R (X, σ ) associated to a symplectic space.(X, σ ) was introduced by D. Buchholz and H. Grundling as a convenient model of the canonical commutation relation (CCR) in quantum mechanics. We first study a representation of.R (Cn, σ ) with the standard symplectic form.σ inside the full Toeplitz algebra over the Fock-Bargmann space. We prove that.R (Cn, σ ) itself is a Toeplitz algebra. In the sense of R. Werner’s correspondence theory, we determine its corresponding shift-invariant and closed space of symbols. Finally, we discuss a representation of the resolvent algebra.R (H, ˜σ ) for an infinite dimensional symplectic separable Hilbert space.(H, ˜σ ). More precisely, we find a representation of.R (H, ˜σ ) inside the full Toeplitz algebra over the Fock-Bargmann space in infinitely many variables.
Keywords
- Correspondence theory, Infinite dimensional phase space, Toeplitz algebra
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
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Semigroups, Algebras and Operator Theory : ICSAOT 2022. ed. / A.A. Ambily; V.B. Kiran Kumar. Springer, 2024. p. 195-228 (Springer Proceedings in Mathematics and Statistics; Vol. 436).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - Resolvent Algebra in Fock-Bargmann Representation
AU - Bauer, Wolfram
AU - Fulsche, Robert
PY - 2024/2/1
Y1 - 2024/2/1
N2 - The resolvent algebra.R (X, σ ) associated to a symplectic space.(X, σ ) was introduced by D. Buchholz and H. Grundling as a convenient model of the canonical commutation relation (CCR) in quantum mechanics. We first study a representation of.R (Cn, σ ) with the standard symplectic form.σ inside the full Toeplitz algebra over the Fock-Bargmann space. We prove that.R (Cn, σ ) itself is a Toeplitz algebra. In the sense of R. Werner’s correspondence theory, we determine its corresponding shift-invariant and closed space of symbols. Finally, we discuss a representation of the resolvent algebra.R (H, ˜σ ) for an infinite dimensional symplectic separable Hilbert space.(H, ˜σ ). More precisely, we find a representation of.R (H, ˜σ ) inside the full Toeplitz algebra over the Fock-Bargmann space in infinitely many variables.
AB - The resolvent algebra.R (X, σ ) associated to a symplectic space.(X, σ ) was introduced by D. Buchholz and H. Grundling as a convenient model of the canonical commutation relation (CCR) in quantum mechanics. We first study a representation of.R (Cn, σ ) with the standard symplectic form.σ inside the full Toeplitz algebra over the Fock-Bargmann space. We prove that.R (Cn, σ ) itself is a Toeplitz algebra. In the sense of R. Werner’s correspondence theory, we determine its corresponding shift-invariant and closed space of symbols. Finally, we discuss a representation of the resolvent algebra.R (H, ˜σ ) for an infinite dimensional symplectic separable Hilbert space.(H, ˜σ ). More precisely, we find a representation of.R (H, ˜σ ) inside the full Toeplitz algebra over the Fock-Bargmann space in infinitely many variables.
KW - Correspondence theory
KW - Infinite dimensional phase space
KW - Toeplitz algebra
UR - http://www.scopus.com/inward/record.url?scp=85186740591&partnerID=8YFLogxK
U2 - 10.1007/978-981-99-6349-2_12
DO - 10.1007/978-981-99-6349-2_12
M3 - Conference contribution
AN - SCOPUS:85186740591
SN - 9789819963485
T3 - Springer Proceedings in Mathematics and Statistics
SP - 195
EP - 228
BT - Semigroups, Algebras and Operator Theory
A2 - Ambily, A.A.
A2 - Kiran Kumar, V.B.
PB - Springer
T2 - International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022
Y2 - 28 March 2022 through 31 March 2022
ER -