Eigenvalue dynamics in the large N Limit of multi matrix systems

Abstract

The Collective Field method is used to investigate various matrix valued problems. First the application to the single hermitian matrix is reviewed after which the method is generalised to multiple hermitian matrices. Two different approaches are considered, both of which return the expected Jacobian. The second approach is then used to explore a system of complex matrices to determine if a Jacobian including both radial and angular dynamics can be revealed. This turns out not to be the case but the analysis is informative, and some avenues for further research are suggested.