Matrix modified Kadomtsev–Petviashvili hierarchy

Using the bilinear formalism, we consider multicomponent and matrix Kadomtsev–Petviashvili hierarchies. The main tool is the bilinear identity for the tau function realized as the vacuum expectation value of a Clifford group element composed of multicomponent fermionic operators. We also construct the Baker–Akhiezer functions and obtain auxiliary linear equations that they satisfy.