#### Document Type

Article

#### Publication Date

2014

#### Keywords

Covariant causal set approach, discrete quantum gravity, shell sequence

#### Abstract

We consider a covariant causal set approach to discrete quantum gravity. We first review the microscopic picture of this approach. In this picture a universe grows one element at a time and its geometry is determined by a sequence of integers called the shell sequence. We next present the macroscopic picture which is described by a sequential growth process. We introduce a model in which the dynamics is governed by a quantum transition amplitude. The amplitude satisfies a stochastic and unitary condition and the resulting dynamics becomes isometric. We show that the dynamics preserves stochastic states. By “doubling down” on the dynamics we obtain a unitary group representation and a natural energy operator. These unitary operators are employed to define canonical position and momentum operators.

#### Recommended Citation

Gudder, S., "An Isometric Dynamics for a Causal Set Approach to Discrete Quantum Gravity" (2014). *Mathematics Preprint Series*. 10.

http://digitalcommons.du.edu/math_preprints/10