International Journal of Theoretical Physics

, Volume 47, Issue 7, pp 1929–1948

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


DOI: 10.1007/s10773-007-9637-2

Cite this article as:
Mallios, A. Int J Theor Phys (2008) 47: 1929. doi:10.1007/s10773-007-9637-2


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.


Quantum relativity Gel’fand/Yoneda transform “Singularities” Sheaf-theoretic dynamics Dynamical relativistic localization Yang-Mills field Topos-theoretic dynamics Topos-theoretic quantum field theory Topological algebra space Topological algebra scheme 

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.University of AthensAthensGreece

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