Geometro-stochastic locality in quantum spacetime and quantum diffusions

Prugovečki, Eduard

doi:10.1007/bf01883565

Cited by 7 publications

(2 citation statements)

References 62 publications

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“…[294,234] and references therein for a comparative discussion of these two approaches). The above construction of geodesic propagation of 'quantum particles' is partially influenced by the works of Drechsler [87,88,89] and Prugovečki [278,279,280,281,282,283,285,284] (see also [123,124]). As opposed to them, we do not require any pseudo-riemannian metric on the base manifold, so we do not introduce soldered Poincaré frame bundles, and we also consider the GNS Hilbert spaces (which may be unitarily inequivalent, if 𝜔 R 𝒩 ‹0 ) varying over the base manifold instead of pasting fibre bundle from identical copies of a single Hilbert space.…”

Section: Local Gauge and Geodesic Propagationmentioning

confidence: 99%

Local quantum information dynamics

Kostecki

2016

Preprint

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This paper is intended to: 1) show how the local smooth geometry of spaces of normal quantum states over W ˚-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path integral approaches; 2) provide a framework for construction of quantum information theories beyond quantum mechanics, such that quantum mechanical linearity holds only locally, while the nonlocal multi-user dynamics exhibits some similarity with general relativity. In the algebraic setting, we propose a method of incorporating nonlinear Poisson and relative entropic local dynamics, as well as local gauge and local source structures, into an effective description of local temporal evolution of quantum states by using fibrewise perturbations of liouvilleans in the fibre bundle of Hilbert spaces over the quantum state manifold. We apply this method to construct an algebraic generalisation of Savvidou's action operator. In the path integral setting, motivated by the Savvidou-Anastopoulous analysis of the role of Kähler space geometry in the Isham-Linden quantum histories, we propose to incorporate local geometry by means of a generalisation of the Daubechies-Klauder coherent state phase space propagator formula. Finally, we discuss the role of Brègman relative entropy in the Jaynes-Mitchell-Favretti renormalisation scheme. Using these tools we show that: 1) the propagation of quantum particles (in Wigner's sense) can be naturally explained as a free fall along the trajectories locally minimising the quantum relative entropy; 2) the contribution of particular trajectories to the global path integral is weighted by the local quantum entropic prior, measuring user's lack of information; 3) the presence of nonlinear quantum control variables results in the change of the curvature of the global quantum state space; 4) the behaviour of zero-point energy under renormalisation of local entropic dynamics is maintained by local redefinition of information mass (prior), which encodes the curvature change. We conclude this work with a proposal of a new framework for nonequilibrium quantum statistical mechanics based on quantum Orlicz spaces, quantum Brègman distances and Banach Lie algebras.

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Section: Local Gauge and Geodesic Propagationmentioning

confidence: 99%

Local quantum information dynamics

Kostecki

2016

Preprint

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“…t5, very briefly summarized in Ref. 16, and based on the earlier work presented in Ref. 17) has been formulated during the span of many years with this type of healthy skepticism in mind, but with an otherwise constructive and progressive type of attitude.…”

Section: I45mentioning

confidence: 99%

Realism, positivism, instrumentalism, and quantum geometry

Prugovečki

1992

Found Phys

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75he roles of classical realism, logical positivism, and pragmatic" instrumentatism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War H developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the "schism" in twentieth century physics created by the Bohr-Einstein "disagreements" on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations .from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of "truth'" in general, or its conventionalistic version in post-World War H quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physies ate reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's "positivism" with Einstein's "reatism" by emphasizing the existence of an underlying quantum reality, in which the), both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by devetop#~g the conceptual and mathematical tools that are most appropriate for such a use.

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Born’s Reciprocity in the Conformal Domain

Jadczyk

1993

Spinors, Twistors, Clifford Algebras and Quantum Deformations

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Geometro-stochastic locality in quantum spacetime and quantum diffusions

Cited by 7 publications

References 62 publications

Local quantum information dynamics

Local quantum information dynamics

Realism, positivism, instrumentalism, and quantum geometry

Born’s Reciprocity in the Conformal Domain

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