An Isometric Dynamics for a Causal Set Approach to Discrete Quantum Gravity

作者：Gudder S^*

来源：International Journal of Theoretical Physics, 2015, 54(12): 4214-4228.

DOI：10.1007/s10773-014-2398-9

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.

• 出版日期2015-12