Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

1 Publication

PT quantum mechanics: finite-dimensional and infinite-dimensional matrix models and their Lie group structures

Günther, U.


Structural features of PT-symmetric quantum mechanical matrix models are discussed: hidden group theoretical aspects, Lie triple systems following from Cartan decompositions of the corresponding Lie algebras, projectivization embeddings to resolve singularities at PT phase transitions. Starting from these structural findings for finite-dimensional PT-symmetric matrix setups, possible technically feasible extensions toward infinite-dimensional Hilbert-Schmidt Lie groups, Fredholm groups and PT-symmetry related Hilbert-Schmidt Grassmannians are sketched. Concrete physical setups where these features show up are briefly discussed.

Keywords: PT symmetry; phase transitions; Lie algebras; Lie triple systems; PT phase transitions; Hilbert-Schmidt Lie groups; Fredholm groups; Hilbert-Schmidt Grassmannians

  • Invited lecture (Conferences)
    15th Conference “Mathematics in Technical and Natural Sciences”, 17.-22.09.2017, Zakopane, Poland