Physics – Quantum Physics
Scientific paper
2006-11-30
Physics
Quantum Physics
This paper was originally written in 1981 and published as a supplement to my Ph.D. thesis. (Davies, P., (1981) The Weyl Algeb
Scientific paper
10.1063/1.2158735
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 in 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.
Bohm D. J.
Davies P. G.
Hiley Basil J.
No associations
LandOfFree
Algebraic Quantum Mechanics and Pregeometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Algebraic Quantum Mechanics and Pregeometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Algebraic Quantum Mechanics and Pregeometry will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-391155