Publication Date
2014
Document Type
Article
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. (2014). An Isometric Dynamics for a Causal Set Approach to Discrete Quantum Gravity. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/10
Comments
This is a post-peer-review, pre-copyedit version of an article published in the International Journal of Theoretical Physics. The final authenticated version is available online at: https://doi.org/10.1007/s10773-014-2398-9