UC Berkeley

The algebraic formulation of large N matrix mechanics recently developed by Halpern and Schwartz leads to a practical method of numerical computation for both action and Hamiltonian problems. The new technique posits a boundary condition on the planar connected parts X_w , namely, that they should decrease rapidly with increasing order. This leads to algebraic and/or variational schemes of computation which show remarkably rapid convergence in numerical tests on some many-matrix models. The method allows the calculation of all moments of the ground state, in a sequence of approximations, and excited states can be determined as well. There are two unexpected findings: a large d expansion and a new selection rule for certain types of interactions.