171 research outputs found
The quantization of gravity in globally hyperbolic spacetimes
We apply the ADM approach to obtain a Hamiltonian description of the
Einstein-Hilbert action. In doing so we add four new ingredients: (i) We
eliminate the diffeomorphism constraints. (ii) We replace the densities by a function \f(x,g_{ij}) with the help of a fixed metric such
that the Lagrangian and hence the Hamiltonian are functions. (iii) We consider
the Lagrangian to be defined in a fiber bundle with base space \so and fibers
F(x) which can be treated as Lorentzian manifolds equipped with the
Wheeler-DeWitt metric. It turns out that the fibers are globally hyperbolic.
(iv) The Hamiltonian operator is a normally hyperbolic operator in the
bundle acting only in the fibers and the Wheeler-DeWitt equation is a
hyperbolic equation in the bundle. Since the corresponding Cauchy problem can
be solved for arbitrary smooth data with compact support, we then apply the
standard techniques of QFT which can be naturally modified to work in the
bundle.Comment: 26 pages, v4: some minor typos corrected, to appear in ATMP 201
A unified quantum theory I: gravity interacting with a Yang-Mills field
Using the results and techniques of a previous paper where we proved the
quantization of gravity we extend the former result by adding a Yang-Mills
functional and a Higgs term to the Einstein-Hilbert action.Comment: v4: minor corrections in some formulas, to appear in ATMP, arXiv
admin note: text overlap with arXiv:1205.1427. text overlap with
arXiv:1205.142
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