  We define and examine certain matrix-valued multiplicative functionals with
local Kato potential terms and use probabilistic techniques to prove that the
semigroups of the corresponding partial differential operators with
matrix-valued coefficients are spatially continuous and have a jointly
continuous integral kernel. These partial differential operators include
Yang-Mills type Hamiltonians and Pauli type Hamiltonians, with "electrical"
potentials that are elements of the matrix-valued local Kato class.
