Algebraic Quantum Mechanics and Pregeometry.

Bohm, D., Davies, P. and Hiley, B., 2006. Algebraic Quantum Mechanics and Pregeometry. In: Quantum Theory: Reconsideration of Foundations - 3, 6-11 June 2005, Vaxjo, Sweden, 314 - 324 .

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Abstract

We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.

Item Type:Conference or Workshop Item (Paper)
Subjects:UNSPECIFIED
Group:Faculty of Science and Technology
ID Code:21620
Deposited By: Unnamed user with email symplectic@symplectic
Deposited On:07 Jan 2015 11:09
Last Modified:22 Jun 2015 15:43

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