arXiv subjects

Oliver Rudolph

Publications and source records attributed to Oliver Rudolph.

22 records · Page 2Linked to original sources

arXiv1996

On the Classification of Decoherence Functionals

The basic ingredients of the consistent histories approach to quantum mechanics are the space of histories and the space of decoherence functionals. In this work we extend the classification theorem for decoherence functionals proven by Isham, Linden and Schreckenberg to the case where the space of histories is the lattice of projection operators on an arbitrary separable or non-separable complex Hilbert space of dimension strictly greater than two.

gr-qc↗

arXiv1996

Consistent Histories and Operational Quantum Physics

In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and give some general comments about it. We investigate to what extent the consistent histories scheme is compatible with the results of the operational formulation of quantum mechanics. According to the operational approach nonrelativistic quantum mechanics is most generally formulated in terms of effects, states and operations. We formulate a generalized consistent histories theory using the concepts and the terminology which have proven useful in the operational formulation of quantum mechanics. The logical rule of the logical interpretation of quantum mechanics is generalized to the present context. The algebraic structure of the generalized theory is studied in detail.

quant-ph↗

arXiv1996

On the Consistent Effect Histories Approach to Quantum Mechanics

A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of `history' is generalized to the notion of `effect history'. The space of effect histories carries the structure of a D-poset. Recent results of J.D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnes' logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author.

quant-ph↗

arXiv1993

Sum-over-histories representation for the causal Green function of free scalar field theory

A set of Green functions ${\cal G}_α(x-y), α\in [0, 2 π[$, for free scalar field theory is introduced, varying between the Hadamard Green function $Δ_1(x-y) \equiv \linebreak[2] \lsta{0} \hspace{-0.1cm} \{ φ(x), φ(y) \} \hspace{-0.1cm} \rsta{0}$ and the causal Green function ${\cal G}_π(x-y) = i Δ(x-y) \equiv [φ(x), φ(y)]$. For every $α\in [0, 2 π[$ a path-integral representation for ${\cal G}_α$ is obtained both in the configuration space and in the phase space of the classical relativistic particle. Especially setting $α= π$ a sum-over-histories representation for the causal Green function is obtained. Furthermore using BRST theory an alternative path-integral representation for ${\cal G}_α$ is presented. From these path integral representations the composition laws for the ${\cal G}_α$'s are derived using a modified path decomposition expansion.

hep-th↗