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Beyond the Quantum

PHASE SPACE DESCRIPTION OF QUANTUM MECHANICS AND NON-COMMUTATIVE GEOMETRY: WINGNER–MOYAL AND BOHM IN A WIDER CONTEXT

Basil J. Hiley

Published Sep 1, 2007• 2 citations
Publisher
DOI
10.1142/9789812771186_0017

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In this paper we discuss the notion of a ‘particle’ and its ‘trajectory’ in the Bohm approach to quantum theory in the context of a non-commutative dynamics which has classical mechanics as a commutative sub-algebra. We study the von Neumann-Moyal algebra and show that the key equations used in the Bohm approach are already contained within this structure. They appear as projections from the non-commutative phase space into space-time. This structure leads us to a more radical view of quantum processes involving individual particles.