相关论文: Another derivation of the geometrical KPZ relation…

In this paper, we extend the heat kernel methods to the first-order formalism of gravity, specifically, in the language of differential forms. This allows us to compute the effective dynamics of 4D gravity when the tetrad degrees of freedom…

Working within the framework of the covariant perturbation theory, we obtain the coincidence limit of the heat kernel of an elliptic second order differential operator that is applicable to a large class of quantum field theories. The basis…

This paper is an overview on our recent results in the calculation of the heat kernel in quantum field theory and quantum gravity. We introduce a deformation of the background fields (including the metric of a curved spacetime manifold) and…

Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…

In these lectures we review our present understanding of the fractal structure of two-dimensional Euclidean quantum gravity coupled to matter.

We provide evidence that the KPZ exponents in two-dimensional quantum gravity can be interpreted as scaling exponents of correlation functions which are functions of the invariant geodesic distance between the fields.

In this paper, we establish the Knizhnik--Polyakov--Zamolodchikov (KPZ) formula of Liouville quantum gravity, using the heat kernel of Liouville Brownian motion. This derivation of the KPZ formula was first suggested by F. David and M.…

A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…

In this paper some techniques useful to perform quantum field theory computations in a covariant manner are reviewed. In particular the background field gauge, the zeta function regularization and the heat kernel approach are highlighted.…

We determine the scaling properties of geometric operators such as lengths, areas, and volumes in models of higher derivative quantum gravity by renormalizing appropriate composite operators. We use these results to deduce the fractal…

We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we verify that the spectral dimension of LQG is 2. Furthermore,…

We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e. the Hall viscosity, the Wen-Zee…

This paper provides explicit pointwise formulas for the heat kernel on compact metric measure spaces that belong to a $(\mathbb{N}\times\mathbb{N})$-parameter family of fractals which are regarded as projective limits of metric measure…

We show that there exists a divergent correlation length in 2d quantum gravity for the matter fields close to the critical point provided one uses the invariant geodesic distance as the measure of distance. The corresponding…

Covariant perturbation expansion is an important method in quantum field theory. In this paper an expansion up to arbitrary order for off-diagonal heat kernels in flat space based on the covariant perturbation expansion is given. In…

A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…

Using our recently proposed covariant algebraic approach the heat kernel for a Laplace-like differential operator in low-energy approximation is studied. Neglecting all the covariant derivatives of the gauge field strength (Yang-Mills…

A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.

We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic…

We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from…