, Volume 47, Issue 7, pp 1929-1948
Date: 03 Jan 2008

\(\mathcal{A}\) -invariance: An Axiomatic Approach to Quantum Relativity

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Abstract

The sort of approach claimed by the title of this article is realizable, at least, within the framework of ADG where we do not assume any “spacetime” supplying the dynamics we employ. The latter classical type of argument can naturally be included herewith along with its concomitant impediments that are emanated therefrom and are essentially “absorbed”, technically speaking, by the proposed mechanism. So our approach, being “manifoldless” (thence, no smoothness, in the standard sense) does not contain any such issue, as before, according to the very definitions, being thus “singularities”-free. As a consequence, the equations that one would be able to formulate within the present set-up will be, by the very essence of the matter, already the quantized ones.

Dedicated to Professor Rafael D. Sorkin on the occasion of his 60th birthday with much friendship and recognition of his creative pursuit in theoretical physics.