A Theory of Quantum Gravity from First Principles
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.
KeywordsQuantum Gravity Boundary Operator Geodesic Distance Strong Ellipticity Elliptic Theory
Unable to display preview. Download preview PDF.
- 2.DeWitt, B.S. (1984): The Space-Time Approach to Quantum Field Theory, in Relativity, Groups and Topology II, ed. by B.S. DeWitt, R. Stora, North-Holland, Amsterdam pp. 381–738Google Scholar
- 5.Hawking, S.W. (1979): The Path-Integral Approach to Quantum Gravity, in General Relativity, an Einstein Centenary Survey, ed. by S.W. Hawking, W Israel, Cambridge University Press, Cambridge, pp. 746–789Google Scholar
- 12.Grubb, G.(1996): Functional Calculus of Pseudodifferential Boundary Problems. Birkhäuser, BostonGoogle Scholar