The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity proper...

The paper concerns linear continuous-variable systems whose state can be measured only through a quantiser. As for an observer the system together with the quantiser behaves like a discrete-event system, the problem of representing this system by some deterministic finite state machine is considered. The main difficulty of this representation problem occurs due to the nondeterminism introduced ...

It has been established that endowing classical phase space with a Riemannian metric is sufficient for describing quantum mechanics. In this letter we argue that, while sufficient, the above condition is certainly not necessary in passing from classical to quantum mechanics. Instead, our approach to quantum mechanics is modelled on a statement that closely resembles Darboux’s theorem for symple...

{ Based on the assumption that a pattern is constructed out of features which are either fully present or absent, we propose a vector quantisation method which constructs patterns using binary combinations of features. For this model there exists an eecient EM-like learning algorithm which learns a set of representative codebook vectors. In terms of a generative model, the collection of allowed...

It is argued that the gauge anomalies are only the artefacts of quantum field theory when certain subtleties are not taken into account. With the Berry's phase needed to satisfy certain boundary conditions of the generating path integral, the gauge anomalies associated with homotopically nontrivial gauge transformations are shown explicitly to be eliminated, without any extra quantum fields int...

Quantisation on spaces with properties of curvature , multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental group representations are used to obtain a direct sum of Hilbert spaces, with a Holonomy method for the non simply connected manifolds.The covering spaces of i...

We formulate the Gupta-Bleuler canonical, covariant and gauge invariant supersymmetric quantization of the supersymmetric (massless) vector field. Our main tool is the recently introduced HilbertKrein structure of the N = 1 superspace.