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arXiv · hep-th/9903131

Infinite Dimensional Free Algebra and the Forms of the Master Field

M. B. Halpern·C. Schwartz
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Abstract

We find an infinite dimensional free algebra which lives at large N in any SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural basis of this algebra is a free-algebraic generalization of Chebyshev polynomials and the dual basis is closely related to the planar connected parts. This leads to a number of free-algebraic forms of the master field including an algebraic derivation of the Gopakumar-Gross form. For action theories, these forms of the master field immediately give a number of new free-algebraic packagings of the planar Schwinger-Dyson equations.

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M. B. Halpern, C. Schwartz. 1999-09-16. Infinite Dimensional Free Algebra and the Forms of the Master Field. https://doi.org/10.1142/s0217751x99002189

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