Infinite Dimensional Free Algebra and the Forms of the Master Field

Details Infinite Dimensional Free Algebra and the Forms of the Master Field Infinite Dimensional Free Algebra and the Forms of the Master Field

1999-03-15

arxiv.org/abs/hep-th/9903131v4

Int.J.Mod.Phys. A14 (1999) 4653-4686

Physics

High Energy Physics

High Energy Physics - Theory

39 pages. Expanded historical remarks

Scientific paper

10.1142/S0217751X99002189

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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