Feynman Rules for Simplicial Gravity

Abstract

We develop the general formalism for performing perturbative diagrammatic expansions in the lattice theory of quantum gravity. The results help establish a precise correspondence between continuum and lattice quantities, and should be a useful guide for non-perturbative studies of gravity. The Feynman rules for Regge's simplicial lattice formulation of gravity are then discussed in detail in two dimensions. As an application, the two-dimensional conformal anomaly due to a $D$-component scalar field is explicitly computed in perturbation theory.

Corrections and references added

References in corpus (11)

• Newtonian Potential in Quantum Regge Gravity
• Potential energy in quantum gravity
• The critical behaviour of Ising spins on 2D Regge lattices
• Faddeev-Popov determinant in 2-dimensional Regge gravity.
• The Well-Defined Phase of Simplicial Quantum Gravity in Four Dimensions
• Discrete Gravity in One Dimension
• On the absence of localized curvature in the weak-coupling phase of quantum gravity
• Fractal Structure in Two-Dimensional Quantum Regge Calculus
• Is There Quantum Gravity in Two Dimensions?
• Dynamically Triangulated Ising Spins in Flat Space
• Random Ising Spins in Two Dimensions - A Flat Space Realization of the KPZ Exponents

Cited by in corpus (5)

• On the Measure in Simplicial Gravity
• Gauge Invariance in Simplicial Gravity
• On the non-perturbative graviton propagator
• On the gravitational diagram technique in the discrete setup
• On the discrete version of the Kerr-Newman solution