1992/02/22 by Lee Smolin · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.1088/0264-9381/9/4/007
published as Class.Quant.Grav.9:883-894,1992 · 14 pages
arxiv created 1992/02/22 · openalex publication_date 1992/04/01 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Using the Ashtekar formulation, it is shown that the G Newton to 0 limit of Euclidean or complexified general relativity is not a free field theory, but is a theory that describes a linearized self-dual connection propagating on an arbitrary anti-self-dual background. This theory is quantized in the loop representation and, as in the full theory, an infinite dimensional space of exact solutions to the constraints are found. An inner product is also proposed. The path integral is constructed from the Hamiltonian theory and the measure is explicitly computed non-perturbatively, without relaying on a semiclassical expansion. This theory could provide the starting point for a new approach to a perturbation theory in G Newton that does not rely on a background field expansion and in which full diffeomorphism invariance is satisfied at each order.