arXiv subjects

Werner Stulpe

Publications and source records attributed to Werner Stulpe.

4 recordsLinked to original sources

arXiv2013

From the Attempt of Certain Classical Reformulations of Quantum Mechanics to Quasi-Probability Representations

The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is revisited, and its limitation in view of a classical reformulation of the statistical scheme of quantum mechanics is discussed. In particular, on the basis of a theorem concerning a non-denseness property of a set of coexistent effects, it is shown that an injective classical embedding of the quantum states cannot be supplemented by an at least approximate classical description of the quantum mechanical effects. As an alternative approach, the concept of quasi-probability representations of quantum mechanics is considered.

quant-ph↗

arXiv2007

The Structure of Classical Extensions of Quantum Probability Theory

On the basis of a suggestive definition of a classical extension of quantum mechanics in terms of statistical models, we prove that every such classical extension is essentially given by the so-called Misra-Bugajski reduction map. We consider how this map enables one to understand quantum mechanics as a reduced classical statistical theory on the projective Hilbert space as phase space and discuss features of the induced hidden-variables model. Moreover, some relevant technical results on the topology and Borel structure of the projective Hilbert space are reviewed.

quant-ph↗

arXiv2007

Topologies and Measurable Structures on the Projective Hilbert Space

A systematic review of the various topologies that can be defined on the projective Hilbert space P(H), i.e., on the set of the pure quantum states, is presented. It is shown that P(H) carries a natural topology as well as a natural measurable structure.

math-ph↗

arXiv2006

Classical Representations of Quantum Mechanics Related to Statistically Complete Observables

We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding is the existence of so-called statistically complete observables and the duality between the state spaces and the spaces of the observables, the latter holding in the quantum as well as in the classical case. In the phase-space context, we further discuss joint position-momentum observables, Hilbert spaces of infinitely differentiable functions on phase space, and dequantizations. Finally, the relation of quantum dynamics to the classical Liouville dynamics is investigated.

quant-ph↗