A Mermin--Wagner theorem on Lorentzian triangulations with quantum spins
| Autor: | Anatoly Yambartsev, Yu. M. Suhov, Mark Kelbert |
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| Rok vydání: | 2012 |
| Předmět: |
Statistics and Probability
Vertex (graph theory) FOS: Physical sciences size-biased critical Galton–Watson branching process Type (model theory) 82B10 82B20 47D08 quantum bosonic system with continuous spins the Feynman–Kac representation symbols.namesake Mermin–Wagner theorem GEOMETRIA DIFERENCIAL reduced density matrix invariance Quantum Mathematical Physics Mathematical physics Mathematics Hilbert space Triangulation (social science) Mathematical Physics (math-ph) Causal Lorentzian triangulations compact Lie group action symbols Quantum gravity FK-DLR equations Distance |
| Zdroj: | Braz. J. Probab. Stat. 28, no. 4 (2014), 515-537 Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| DOI: | 10.48550/arxiv.1211.5446 |
| Popis: | We consider infinite random casual 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 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. Comment: 28 pages, 1 figure |
| Databáze: | OpenAIRE |
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