2000/02/08 by Giampiero Esposito, Esposito, Giampiero · 4 citations
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0002033
15 pages, plain Tex. In the revised version, the part after Eq. (38) is completely new
openalex publication_date 2000/02/08 · arxiv created 2000/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When quantum fields are studied on manifolds with boundary, the corresponding one-loop quantum theory for bosonic gauge fields with linear covariant gauges needs the assignment of suitable boundary conditions for elliptic differential operators of Laplace type. There are however deep reasons to modify such a scheme and allow for pseudo-differential boundary-value problems. When the boundary operator is allowed to be pseudo-differential while remaining a projector, the conditions on its kernel leading to strong ellipticity of the boundary-value problem are studied in detail. This makes it possible to develop a theory of one-loop quantum gravity from first principles only, i.e. the physical principle of invariance under infinitesimal diffeomorphisms and the mathematical requirement of a strongly elliptic theory.