We consider infinite random causal Lorentzian triangulations emerging in quantum gravity for critical values of parameters. With each vertex of the triangulation we associate a Hilbert space representing a bosonic particle moving in accordance with the standard laws of Quantum Mechanics. The particles interact via two-body potentials decaying with the graph distance. A Mermin-Wagner type theorem is proven for infinite-volume reduced density matrices related to solutions to DLR equations in the Feynman-Kac (FK) representation.
|Original language||English (US)|
|Number of pages||23|
|Journal||Brazilian Journal of Probability and Statistics|
|State||Published - Nov 2014|
All Science Journal Classification (ASJC) codes
- Statistics and Probability