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The rationale for introducing non-hermitian Hamiltonians and other observables is reviewed and open issues identified. We present a new approach based on Moyal products to compute the metric for quasi-hermitian systems. This approach is not only an efficient method of computation, but also suggests a new perspective on quasi-hermitian quantum mechanics which invites further exploration. In particular, we present some first results which link the Berry connection and curvature to non-perturbative properties and the metric.
Bell suggested that a new perspective on quantum mechanics was needed. We propose a solution of the measurement problem based on a reconsideration of the nature of particles. The solution is presented with an idealized model involving non-locality or
In 1956 Dyson analyzed the low-energy excitations of a ferromagnet using a Hamiltonian that was non-Hermitian with respect to the standard inner product. This allowed for a facile rendering of these excitations (known as spin waves) as weakly interac
Using the notions of frame transform and of square integrable projective representation of a locally compact group $G$, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert spa
Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $eta$ operators. We show that despite th
$mathcal{PT}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $mathcal{PT}$-symmetric systems, with a number of $mathcal{PT}$-symmetry related applications. This line of resea