Communications in Mathematical Physics

, Volume 148, Issue 3, pp 469–485 | Cite as

The solution space of the unitary matrix model string equation and the Sato Grassmannian

  • Konstantinos N. Anagnostopoulos
  • Mark J. Bowick
  • Albert Schwarz
Article

Abstract

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 pointsV1 andV2 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
matrices of differential operators. These conditions onV1 andV2 yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraintsL n (n≧0), whereL n annihilate the two modified-KdV τ-functions whose product gives the partition function of the Unitary Matrix Model.

Keywords

Differential Equation Neural Network Complex System Partition Function Nonlinear Dynamics 

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Konstantinos N. Anagnostopoulos
    • 1
  • Mark J. Bowick
    • 1
  • Albert Schwarz
    • 2
  1. 1.Physics DepartmentSyracuse UniversitySyracuseUSA
  2. 2.Department of MathematicsUniversity of CaliforniaDavisUSA

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