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The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz
The Solution Space Of The Unitary Matrix Model String Equation And The Sato Grassmannian, Konstantinos N. Anagnostopoulos, Mark Bowick, Albert Schwarz
Physics - All Scholarship
The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equation is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P; Q \Gamma ] = 1, with P and Q \Gamma 2 \Theta 2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations …
An Operator Formalism For Unitary Matrix Models, Konstantinos N. Anagnostopoulos, Mark Bowick, N. Ishibashi
An Operator Formalism For Unitary Matrix Models, Konstantinos N. Anagnostopoulos, Mark Bowick, N. Ishibashi
Physics - All Scholarship
We analyze the double scaling limit of unitary matrix models in terms of trigonometric orthogonal polynomials on the circle. In particular we find a compact formulation of the string equation at the k th multicritical point in terms of pseudo-differential operators and a corresponding action principle. We also relate this approach to the mKdV hierarchy which appears in the analysis in terms of conventional orthogonal polynomials on the circle.