Free Variables and the Two Matrix Model

Abstract

We study the full set of planar Green's functions for a two-matrix model using the language of functions of non-commuting variables. Both the standard Schwinger-Dyson equations and equations determining connected Green's functions can be efficiently discussed and solved. This solution determines the master field for the model in the `$C$-representation.'

8 pages, harvmac

References in corpus (3)

• Mastering the Master Field
• Stochastic Master Fields
• Loop Space Hamiltonians And Field Theory Of Non-Critical Strings

Cited by in corpus (25)

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• The Algebras of Large N Matrix Mechanics
• A geometric approach to free variable loop equations in discretized theories of 2D gravity
• A causal perspective on random geometry
• Infinite Dimensional Free Algebra and the Forms of the Master Field
• Large $N$ Solution of the 2D Supersymmetric Yang-Mills Theory
• The Ising model with a boundary magnetic field on a random surface
• Spin/disorder correlations and duality in the c=1/2 string
• Entropy of Operator-valued Random Variables: A Variational Principle for Large N Matrix Models
• Boundary fields and renormalization group flow in the two-matrix model
• Multi-matrix loop equations: algebraic & differential structures and an approximation based on deformation quantization
• The Master Field for Rainbow Diagrams and Free Non-Commutative Random Variables
• Non-anomalous `Ward' identities to supplement large-N multi-matrix loop equations for correlations
• The Master Field For 2D QCD On The Sphere
• Noncommutative probability, matrix models, and quantum orbifold geometry
• Schwinger-Dyson operator of Yang-Mills matrix models with ghosts and derivations of the graded shuffle algebra
• Relativistic Theory of Infinite Statistics Fields
• Large-N Limit as a Classical Limit: Baryon in Two-Dimensional QCD and Multi-Matrix Models
• Ward-Takahashi Identities in Large N Field Theories
• The Master Field for the Half-Planar Approximation for Large $N$ Matrix Models and Boltzmann Field Theory