Authors

Stan Gudder

Document Type

Article

Publication Date

2013

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.

Included in

Mathematics Commons

Share

COinS