Bohm, D., Davies, P. and Hiley, B., 2006. Algebraic Quantum Mechanics and Pregeometry. In: Quantum Theory: Reconsideration of Foundations  3, 611 June 2005, Vaxjo, Sweden, 314  324 .
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Abstract
We discuss the relation between the qnumber approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the qnumbers 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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