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Which metrics are consistent with a given pseudo-hermitian matrix?
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SYSNO ASEP 0553621 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Which metrics are consistent with a given pseudo-hermitian matrix? Author(s) Feinberg, J. (IL)
Znojil, Miloslav (UJF-V) RID, ORCID, SAINumber of authors 2 Article number 013505 Source Title Journal of Mathematical Physics. - : AIP Publishing - ISSN 0022-2488
Roč. 63, č. 1 (2022)Number of pages 5 s. Publication form Print - P Language eng - English Country US - United States Keywords pseduo-hermitian ; matrix ; eigenvalues OECD category Pure mathematics Method of publishing Limited access Institutional support UJF-V - RVO:61389005 UT WOS 000747485800004 EID SCOPUS 85123572712 DOI 10.1063/5.0079385 Annotation Given a diagonalizable N x N matrix H, whose non-degenerate spectrum consists of p pairs of complex conjugate eigenvalues and additional N - 2p real eigenvalues, we determine all metrics M, of all possible signatures, with respect to which H is pseudo-hermitian. In particular, we show that any compatible M must have p pairs of opposite eigenvalues in its spectrum so that p is the minimal number of both positive and negative eigenvalues of M. We provide explicit parameterization of the space of all admissible metrics and show that it is topologically a p-dimensional torus tensored with an appropriate power of the group Z(2). Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2023 Electronic address https://doi.org/10.1063/5.0079385
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