On the curvature of a certain riemannian space of matrices

Peter Michor; Dénes Petz; Attila Andai

On the curvature of a certain riemannian space of matrices

Peter Michor
, Dénes Petz
, Attila Andai

Institut für Mathematik

Veröffentlichungen: Beitrag in Fachzeitschrift › Artikel › Peer Reviewed

Abstract

Positive definite matrices of trace 1 describe the state space of a finite quantum system. This manifold can be endowed by the physically relevant Bogoliubov-Kubo-Mori inner product as a Riemannian metric. In this paper the curvature tensor and the scalar curvature are computed.

Originalsprache	Englisch
Seiten (von - bis)	199-212
Seitenumfang	14
Fachzeitschrift	Infinite Dimensional Analysis, Quantum Probability and Related Topics (IDAQP)
Jahrgang	3
Ausgabenummer	2
Publikationsstatus	Veröffentlicht - 2000

ÖFOS 2012

1010 Mathematik

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abstract = "Positive definite matrices of trace 1 describe the state space of a finite quantum system. This manifold can be endowed by the physically relevant Bogoliubov-Kubo-Mori inner product as a Riemannian metric. In this paper the curvature tensor and the scalar curvature are computed.",

author = "Peter Michor and D{\'e}nes Petz and Attila Andai",

note = "Affiliations: Institut f{\"u}r Mathematik, Universit{\"a}t Wien, Strudlhofgasse 4, A-1090 Wien, Austria; Erwin Schrodinger Intl. Inst. M., Boltzmanngasse 9, A-1090 Wien, Austria; Institute of Mathematics, Technical University Budapest, Sztoczek u. 2, H-1521 Budapest XI, Hungary Adressen: Michor, P.W.; Institut f{\"u}r Mathematik; Universit{\"a}t Wien; Strudlhofgasse 4 A-1090 Wien, Austria; email: [email protected] Source-File: 506Scopus.csv Import aus Scopus: 2-s2.0-0034419012 Importdatum: 24.01.2007 11:28:18 22.10.2007: Datenanforderung 1920 (Import Sachbearbeiter) 04.01.2008: Datenanforderung 2054 (Import Sachbearbeiter)",

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language = "English",

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pages = "199--212",

journal = "Infinite Dimensional Analysis, Quantum Probability and Related Topics (IDAQP)",

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AU - Michor, Peter

AU - Petz, Dénes

AU - Andai, Attila

N1 - Affiliations: Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria; Erwin Schrodinger Intl. Inst. M., Boltzmanngasse 9, A-1090 Wien, Austria; Institute of Mathematics, Technical University Budapest, Sztoczek u. 2, H-1521 Budapest XI, Hungary Adressen: Michor, P.W.; Institut für Mathematik; Universität Wien; Strudlhofgasse 4 A-1090 Wien, Austria; email: [email protected] Source-File: 506Scopus.csv Import aus Scopus: 2-s2.0-0034419012 Importdatum: 24.01.2007 11:28:18 22.10.2007: Datenanforderung 1920 (Import Sachbearbeiter) 04.01.2008: Datenanforderung 2054 (Import Sachbearbeiter)

PY - 2000

Y1 - 2000

N2 - Positive definite matrices of trace 1 describe the state space of a finite quantum system. This manifold can be endowed by the physically relevant Bogoliubov-Kubo-Mori inner product as a Riemannian metric. In this paper the curvature tensor and the scalar curvature are computed.

AB - Positive definite matrices of trace 1 describe the state space of a finite quantum system. This manifold can be endowed by the physically relevant Bogoliubov-Kubo-Mori inner product as a Riemannian metric. In this paper the curvature tensor and the scalar curvature are computed.

M3 - Article

SN - 0219-0257

VL - 3

SP - 199

EP - 212

JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics (IDAQP)

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics (IDAQP)

IS - 2

ER -

On the curvature of a certain riemannian space of matrices

Abstract

ÖFOS 2012

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