Publications Repository  HelmholtzZentrum DresdenRossendorf
A few remarks on the structure of PT quantum mechanics
Günther, U.
In the first part of the talk, starting from a historical discussion of the 2dimensional Ising model, the YangLee analysis of the zeros of the corresponding partition function and the occurrence of the YangLee edge singularities the structural origin of the quantum mechanical toy model Hamiltonian with ix^3 potential is elucidated. The close relationship of this Hamiltonian to the Landau theory of phase transitions and conformal field theories (CFTs) is sketched what provides an intuitive explanation for the operatortheoretic difficulties in treating a conjectured Hermitian structure of the ix^3 model in full depth.
In the second part of the talk, the Krein space and Hilbert space metric structures of quasiHermitian PTsymmetric matrix models are discussed with emphasis on the underlying general Lie group structures of these metric operators. The Cartan decomposition into compact and noncompact metric components is used to show the existence of an underlying Lie triple system and its relation to the curvature of homogeneous coset spaces.
Finally, several extension schemes from finitedimensional Lie groups toward ∞−dimensional Lie groups and HilbertSchmidt Lie groups are sketched.
Keywords: YangLee model; YangLee edge singularity; Ising model; Landau theory of phase transitions; conformal field theory; PT quantum mechanics; metric operator; Krein space; Lie groups; Cartan decomposition; Lie triple systems; homogeneous coset spaces; HilbertSchmidt Lie groups

Invited lecture (Conferences)
14th International Workshop on PseudoHermitian Hamiltonians in Quantum Physics, 05.10.09.2014, Setif, Algeria
Permalink: https://www.hzdr.de/publications/Publ21174
Publ.Id: 21174