Results 1 - 10 of 8414
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[en] The technique of regularization by dimensional reduction is applied to source-free quantum gravity. The one-loop counterterms for the effective gravity-matter system are calculated in the background field formalism. The ersatz matter fields which arise in this regularization scheme are found to have no effect on the renormalizability of the theory. (orig.)
[en] The dimensionful nature of the coupling in the Einstein-Hilbert action in four dimensions implies that the theory is non-renormalizable; explicit calculation shows that beginning at two loop order, divergences arise that cannot be removed by renormalization without introducing new terms in the classical action. It has been shown that, by use of a Lagrange multiplier field to ensure that the classical equation of motion is satisfied in the path integral, radiative effects can be restricted to one-loop order. We show that by use of such Lagrange multiplier fields, the Einstein-Hilbert action can be quantized without the occurrence of non-renormalizable divergences. We then apply this mechanism to a model in which there is in addition to the Einstein-Hilbert action, a fully covariant action for a self-interacting scalar field coupled to the metric. It proves possible to restrict loop diagrams involving internal lines involving the metric to one-loop order; diagrams in which the scalar field propagates occur at arbitrary high order in the loop expansion. This model also can be shown to be renormalizable. Incorporating spinor and vector fields in the same way as scalar fields is feasible, and so a fully covariant Standard Model with a dynamical metric field can also be shown to be renormalizable. (author)
[en] Although the wish to unify theories into something more fundamental is omnipresent and compelling, nonetheless, in a sense, theories must first be “unifiable.” The reasons for the success of the unification of electricity and magnetism into a theory of electromagnetism are contrasted with the reasons for the failure of the Einstein-Maxwell unification of gravitation and electromagnetism and the attempts of quantum gravity to unify Einstein’s theory of gravity with quantum field theory. The difference between a unification of two theories, a concatenation of them, and the existence of a formal analogy between them is also discussed. (paper)
[en] The simplicial framework of Engle-Pereira-Rovelli-Livine spin-foam models is generalized to match the diffeomorphism invariant framework of loop quantum gravity. The simplicial spin-foams are generalized to arbitrary linear 2-cell spin-foams. The resulting framework admits all the spin-network states of loop quantum gravity, not only those defined by triangulations (or cubulations). In particular, the notion of embedded spin-foam we use allows us to consider knotting or linking spin-foam histories. Also the main tools, the vertex structure and the vertex amplitude, are naturally generalized to an arbitrary valency case. The correspondence between all the SU(2) intertwiners and the SU(2)xSU(2) EPRL intertwiners is proved to be 1-1 in the case of the Barbero-Immirzi parameter |γ| ≥ 1.