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

Abstract

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.

32 pages, plain TeX, no figures

References in corpus (3)

• Minimal Length Uncertainty Relation and Ultraviolet Regularisation
• Poincaré Supersymmetry Representations Over Trace Class Noncommutative Graded Operator Algebras
• The Matrix Model for M Theory as an Exemplar of Trace (or Generalized Quantum) Dynamics

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• Incorporating gravity into trace dynamics: the induced gravitational action
• Jacobson generators, Fock representations and statistics of sl(n+1)
• Maximally localized states and causality in non commutative quantum theories