A Mermin-Wagner theorem on Lorentzian triangulations with quantum spins

M. Kelbert, Yu Suhov, A. Yambartsev

Research output: Contribution to journalArticle

Abstract

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 languageEnglish (US)
Pages (from-to)515-537
Number of pages23
JournalBrazilian Journal of Probability and Statistics
Volume28
Issue number4
DOIs
Publication statusPublished - Nov 2014

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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