Publication Date
2013
Document Type
Article
Keywords
Causal set approach, Discrete quantum gravity, Quantum sequential growth process
Abstract
This paper is based on the causal set approach to discrete quantum gravity. We first describe a classical sequential growth process (CSGP) in which the universe grows one element at a time in discrete steps. At each step the process has the form of a causal set (causet) and the “completed” universe is given by a path through a discretely growing chain of causets. We then quantize the CSGP by forming a Hilbert space H on the set of paths. The quantum dynamics is governed by a sequence of positive operators ρn on H that satisfy normalization and consistency conditions. The pair (H, {ρn}) is called a quantum sequential growth process (QSGP). We next discuss a concrete realization of a QSGP in terms of a natural quantum action. This gives an amplitude process related to the “sum over histories” approach to quantum mechanics. Finally, we briefly discuss a discrete form of Einstein’s field equation and speculate how this may be employed to compare the present framework with classical general relativity theory.
Recommended Citation
Gudder, S. (2013). A Dynamics for Discrete Quantum Gravity. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/24
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/s10773-013-1940-5