Corrections to the Emergent Canonical Commutation Relations Arising in the Statistical Mechanics of Matrix Models

Details Corrections to the Emergent Canonical Commutation Relations Arising in the Statistical Mechanics of Matrix Models Corrections to the Emergent Canonical Commutation Relations Arising in the Statistical Mechanics of Matrix Models

1997-09-15

arxiv.org/abs/hep-th/9709106v2

J.Math.Phys. 39 (1998) 5083-5097

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, plain TeX, no figures

Scientific paper

10.1063/1.532579

We study the leading corrections to the emergent canonical commutation relations arising in the statistical mechanics of matrix models, by deriving several related Ward identities, and give conditions for these corrections to be small. We show that emergent canonical commutators are possible only in matrix models in complex Hilbert space for which the numbers of fermionic and bosonic fundamental degrees of freedom are equal, suggesting that supersymmetry will play a crucial role. Our results simplify, and sharpen, those obtained earlier by Adler and Millard.

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