CORRECTIONS TO THE EMERGENT CANONICAL COMMUTATION RELATIONS ARISING IN THE STATISTICAL-MECHANICS OF MATRIX MODELS

We study the leading corrections to the emergent canonical commutation relations arising in the statistical mechanics of matrix models, by d eriving 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 ar e equal, suggesting that supersymmetry will play a crucial role. Our r esults simplify, and sharpen, those obtained earlier by Adler and Mill ard. (C) 1998 American Institute of Physics. [S0022-2488(98)03310-6].