A Dynamics for Discrete Quantum Gravity

作者：Gudder S^*

来源：International Journal of Theoretical Physics, 2014, 53(10): 3575-3586.

DOI：10.1007/s10773-013-1940-5

• Quantum processes
• Quantum gravity
• Causal sets

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 %26quot;completed%26quot; 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 rho (n) on H that satisfy normalization and consistency conditions. The pair (H,{rho (n) }) 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 %26quot;sum over histories%26quot; approach to quantum mechanics. Finally, we briefly discuss a discrete form of Einstein%26apos;s field equation and speculate how this may be employed to compare the present framework with classical general relativity theory.

• 出版日期2014-10