Correlation functions for multi-matrix models and quaternion determinants Original Research Article

Using a close relationship to the Brownian motion model of random matrices, multi-matrix models in quantum field theory are analyzed. In the case many hermitian matrices are connected in a chain and one of them has a restricted (real symmetric, self dual real quaternion or antisymmetric hermitian) symmetry, the multi-matrix multi-level correlation functions are shown to have quaternion determinant forms.