Which metrics are consistent with a given pseudo-hermitian matrix?

0553621 - ÚJF 2023 RIV US eng J - Článek v odborném periodiku
Feinberg, J. - Znojil, Miloslav
Which metrics are consistent with a given pseudo-hermitian matrix?
Journal of Mathematical Physics. Roč. 63, č. 1 (2022), č. článku 013505. ISSN 0022-2488. E-ISSN 1089-7658
Institucionální podpora: RVO:61389005
Klíčová slova: pseduo-hermitian * matrix * eigenvalues
Obor OECD: Pure mathematics
Impakt faktor: 1.3, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1063/5.0079385

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).
Trvalý link: http://hdl.handle.net/11104/0328375