In the context of quasi-Hermitian theories, which are non-Hermitian in the conventional sense, but can be made Hermitian by the introduction of a dynamically-determined metric η, we address the problem of how the functional integral and the Feynman diagrams deduced therefrom “know” about the metric. Our investigation is triggered by a result of Bender, Chen and Milton, who calculated perturbati...

We show that a quantum system possessing an exact antilinear symmetry, in particular PT -symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian Hamiltonian with exact PT -symmetry to a Hermitian Hamiltonian. We apply our general results to PT symmetry in finite-dimensions and give the explicit form of the...

We construct a concrete realization of the generalized parity (P), time-reversal (T ), and charge-conjugation (C) operators, that were initially defined in the study of the PT symmetric and pseudo-Hermitian Hamiltonians, for Klein-Gordon fields. We show that PT and C operators, that signify certain symmetries of the system, correspond to the ordinary time-reversal and charge-conjugation transfo...

We describe a new extension to ScaLAPACK [2] for computing with symmetric (Hermi-tian) matrices stored in a packed form. The new code is built upon the ScaLAPACK routines for full dense storage for a high degree of software reuse. The original ScaLAPACK stores a symmetric matrix as a full matrix but accesses only the lower or upper triangular part. The new code enables more efficient use of mem...

Transmission eigenvalues have important applications in inverse scattering theory. They can be used to obtain useful information of the physical properties, such as the index of refraction, of the scattering target. Despite considerable effort devoted to the existence and estimation for the transmission eigenvalues, the numerical treatment is limited. Since the problem is non-standard, classica...

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass η-weak-pseudo-Hermitian Hamiltonians. Two ”user -friendly” reference-target maps are introduced to serve for exactsolvability of some non-Hermitian η-weak-pseudo-Hermitian position dependent mass Hamiltonians. A non-Hermitian PT -...