Brazilian Journal of Probability and Statistics

A Mermin–Wagner theorem on Lorentzian triangulations with quantum spins

M. Kelbert, Yu. Suhov, and A. Yambartsev

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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.

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Braz. J. Probab. Stat., Volume 28, Number 4 (2014), 515-537.

First available in Project Euclid: 30 July 2014

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Causal Lorentzian triangulations size-biased critical Galton–Watson branching process quantum bosonic system with continuous spins compact Lie group action the Feynman–Kac representation FK-DLR equations reduced density matrix invariance


Kelbert, M.; Suhov, Yu.; Yambartsev, A. A Mermin–Wagner theorem on Lorentzian triangulations with quantum spins. Braz. J. Probab. Stat. 28 (2014), no. 4, 515--537. doi:10.1214/13-BJPS222.

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