Related papers: Path integral measure in Regge calculus from the f…
Integration by parts formulae are given for a class of measures on the space of paths of a smooth manifold $M$ determined by the laws of degenerate diffusions. The mother of such formulae, on the path space of diffeomorphism group of $M$ is…
Any theory can be made Weyl invariant by introducing a dilaton. It is shown how to construct renormalization group equations for gravity that maintain this property. Explicit calculations are given only in the simplest approximation, namely…
In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field…
We review a new prescription for calculating the Lagrangian path integral measure directly from the Hamiltonian Schwinger-Dyson equations. The method agrees with the usual way of deriving the measure in which one has to perform the path…
Two-loop Feynman integrals of the massive $\phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric…
We investigate threshold phenomena in weighted $\ell^2$-spaces and characterize the critical regimes where elements with either small support or maximally bad range can be constructed. Our results are shown to be optimal in several…
We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is…
The path integral of four dimensional quantum gravity is restricted to conformally self-dual metrics. It reduces to integrals over the conformal factor and over the moduli space of conformally self--dual metrics and can be studied with the…
Path integral quantization of quantum gauge general relativity is discussed in this paper. First, we deduce the generating functional of green function with external fields. Based on this generating functional, the propagators of…
We study the quantization of two versions of unimodular gravity, namely, fully diffeomorphism-invariant unimodular gravity and unimodular gravity with fixed metric determinant utilizing standard path integral approach. We derive the BRST…
In this paper we suggest gauge invariant discretization of Poincare quantum gravity. We generalize Regge calculus to the case of Riemann-Cartan space. The basic element of the constructed discretization is piecewize linear Riemann-Cartan…
We consider spinfoam quantum gravity on a spacetime decomposition with many 4-simplices, in the double scaling limit in which the Immirzi parameter $\gamma$ is sent to zero (flipped limit) and the physical area in Planck units ($\gamma$…
The point pair function $p_G$ defined in a domain $G\subsetneq\mathbb{R}^n$ is shown to be a quasi-metric and its other properties are studied. For a convex domain $G\subsetneq\mathbb{R}^n$, a new intrinsic quasi-metric called the function…
Starting from an action for discretized gravity we derive a canonical formalism that exactly reproduces the dynamics and (broken) symmetries of the covariant formalism. For linearized Regge calculus on a flat background -- which exhibits…
At first, we consider the path integral method for the covariant symmetry breaking in gravity. We replace the scalar fields, instead of the degrees of freedom which have been removed by gauge fixing constraints. Finally the specific ghost…
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and…
We apply a recently developed dispersive formalism to calculate the Regge trajectories of the $f_2(1270)$ and $f_2'(1525)$ mesons. Trajectories are calculated, not fitted to a family of resonances. Assuming that these spin-2 resonances can…
The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…
In the Faddeev formulation of gravity, the metric is regarded as composite field, bilinear of $d = 10$ 4-vector fields. We derive the minisuperspace (discrete) Faddeev action by evaluating the Faddeev action on the spacetime composed of the…
The 4D Regge action is invariant under 5--1 and 4--2 Pachner moves, which define a subset of (local) changes of the triangulation. Given this fact one might hope to find a local path integral measure that makes the quantum theory invariant…