Related papers: Path Integral Over Conformally Self-Dual Geometrie…
The path integral for higher-derivative quantum gravity with torsion is considered. Applying the methods of two-dimensional quantum gravity, this path integral is analyzed in the limit of conformally self-dual metrics. A scaling law for…
The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…
In this paper, two things are done. (i) Using cohomological techniques, we explore the consistent deformations of linearized conformal gravity in 4 dimensions. We show that the only possibility involving no more than 4 derivatives of the…
We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as integrals over the SL(2, R) invariant Gaussian functional measure. We reduce these path integrals to the products of Wiener path…
We present an extension to arbitrary dimensions of a worldline path integral approach to one-loop quantum gravity, which was previously formulated in four spacetime dimensions. By utilizing this method, we recalculate gauge invariant…
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the…
A proper definition of the path integral of quantum gravity has been a long-standing puzzle because the Weyl factor of the Euclidean metric has a wrong-sign kinetic term. We propose a definition of two-dimensional Liouville quantum gravity…
In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a…
We study the quantum aspects of the conformal gravity in four dimensions, specifically addressing a known discrepancy in beta functions between general quadratic curvature theories and conformal gravity, which corresponds to two scalar…
We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…
We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphism-invariant theory is analyzed, which does not include a unimodular condition on the metric, while still being equivalent to other…
A system of gravity coupled to a 2-form gauge field, a dilaton and Yang-Mills fields in $2n$ dimensions arises from the (2,1) sigma model or string. The field equations imply that the curvature with torsion and Yang-Mills field strength are…
We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a…
We propose that a class of new topologies, for which there is no classical solution, should be included in the path integral of three-dimensional pure gravity, and that their inclusion solves pathological negativities in the spectrum,…
We review recent developments in physical implications of Weyl conformal geometry. The associated Weyl quadratic gravity action is a gauge theory of the Weyl group of dilatations and Poincar\'e symmetry. Weyl conformal geometry is defined…
In this thesis we analyze a very simple model of two dimensional quantum gravity based on causal dynamical triangulations (CDT). We present an exactly solvable model which indicates that it is possible to incorporate spatial topology…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…
Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a…
A method is presented which restricts the space of paths entering the path integral of quantum mechanics to subspaces of $C^\alpha$, by only allowing paths which possess at least $\alpha$ derivatives. The method introduces two external…
The theory of embedded random surfaces, equivalent to two--dimensional quantum gravity coupled to matter, is reviewed, further developed and partly generalized to four dimensions. It is shown that the action of the Liouville field theory…