2006/06/28 by Ioannis Raptis
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Canonical quantization #Classical unified field theories #Einstein #Gauge theory #General relativity #Introduction to gauge theory #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #Quantum gravity #Sheaf #Spacetime #gr-qc
paper · pdf · doi:10.1007/s10773-006-9263-4
published as Int.J.Theor.Phys.46:1137-1181,2007 · 43 pages; latest version contributed to a fest-volume celebrating Rafael Sorkin's 60th birthday (Erratum: in earlier versions I had wrongly written that the Editor for this volume is Daniele Oriti, with CUP as publisher. I apologize for the mistake.)
arxiv created 2006/06/28 · openalex publication_date 2007/02/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.