caa a22 4500 463197445 CHVBK 20180406164926.0 cr unu---uuuuu 170326e20070501xx s 000 0 eng 10.1007/s10773-006-9263-4 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9263-4 Raptis Ioannis Department of Mathematics, University of Athens, Panepistimioupolis, 157 84, Athens, Greece aut ‘Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories [Elektronische Daten] [Ioannis Raptis] Certain pivotal results from various applications of Abstract Differential Geometry (ADG) to gravity and gauge theories are presently collected and used to argue that we already possess a geometrically (pre)quantized, second quantized and manifestly background spacetime manifold independent vacuum Einstein gravitational field dynamics. The arguments carry also mutatis mutandis to the case of free Yang-Mills theories, since from the ADG-theoretic perspective gravity is regarded as another gauge field theory. The powerful algebraico-categorical, sheaf cohomological conceptual and technical machinery of ADG is then employed, based on the fundamental ADG-theoretic conception of a field as a pair ( $${\mathcal{E}},{\mathcal{D}}$$ ) consisting of a vector sheaf $${\mathcal{E}}$$ and an algebraic connection $${\mathcal{D}}$$ acting categorically as a sheaf morphism on $${\mathcal{E}}$$ 's local sections, to introduce a ‘universal', because expressly functorial, field quantization scenario coined third quantization. Although third quantization is fully covariant, on intuitive and heuristic grounds alone it formally appears to follow a canonical route; albeit, in a purely algebraic and, in contradistinction to geometric (pre)quantization and (canonical) second quantization, manifestly background geometrical spacetime manifold independent fashion, as befits ADG. All in all, from the ADG-theoretic vantage, vacuum Einstein gravity and free Yang-Mills theories are regarded as external spacetime manifold unconstrained, third quantized, pure gauge field theories. The paper abounds with philosophical smatterings and speculative remarks about the potential import and significance of our results to current and future Quantum Gravity research. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work. Springer Science+Business Media, LLC, 2007 quantum gravity nationallicence quantum gauge theories nationallicence geometric (pre)quantization nationallicence second quantization nationallicence abstract differential geometry nationallicence sheaf theory nationallicence sheaf cohomology nationallicence category theory nationallicence International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/5(2007-05-01), 1137-1181 0020-7748 46:5<1137 2007 46 10773 https://doi.org/10.1007/s10773-006-9263-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9263-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Raptis Ioannis Department of Mathematics, University of Athens, Panepistimioupolis, 157 84, Athens, Greece aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 46/5(2007-05-01), 1137-1181 0020-7748 46:5<1137 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer