`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories

Details `Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories `Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories

2006-06-04

arxiv.org/abs/gr-qc/0606021v4

Int.J.Theor.Phys.46:1137-1181,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

43 pages; latest version contributed to a fest-volume celebrating Rafael Sorkin's 60th birthday (Erratum: in earlier versions

Scientific paper

10.1007/s10773-006-9263-4

Based on the algebraico-categorical (:sheaf-theoretic and sheaf cohomological) conceptual and technical machinery of Abstract Differential Geometry, a new, genuinely background spacetime manifold independent, field quantization scenario for vacuum Einstein gravity and free Yang-Mills theories is introduced. The scheme is coined `third quantization' and, although it formally appears to follow a canonical route, it is fully covariant, because it is an expressly functorial `procedure'. Various current and future Quantum Gravity research issues are discussed under the light of 3rd-quantization. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work.

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