Gauge fixing in Causal Dynamical Triangulations

Two - dimensional causal dynamical triangulations with gauge fields

A statistical formalism of Causal Dynamical Triangulations

We rewrite the 1+1 Causal Dynamical Triangulations model as a spin system and thus provide a new method of solution of the model. Email address: [email protected] Email address: [email protected] 1

Gauge fixing in (2+1)-gravity with vanishing cosmological constant

We apply Dirac’s gauge fixing procedure to (2+1)-gravity with vanishing cosmological constant. For general gauge fixing conditions based on two point particles, this yields explicit expressions for the Dirac bracket. We explain how gauge fixing is related to the introduction of an observer into the theory and show that the Dirac bracket is determined by a classical dynamical r-matrix. Its two d...

Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry

We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac’s gauge fixing procedure, we implement the constraints and determine the Dirac bracket on the gauge-invariant phase space. The chosen gauge fixing conditions have a natural physical interpretation and specify an observer in the spacetime. We derive explicit expressions for the res...

(2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations

We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an additional notion of order on the discrete, causal geometries. This simplifies the combinatorial problem of counting geometries just enough to enable us to c...