  On the basis of the canonical quantization procedure of a system defined on a
cubic lattice, we propose a new method, in which resolutions of unity expressed
in terms of eigenvectors are naturally provided, to find eigenvectors of field
operators. By making use of fundamental ingredients thus obtained, we derive
time sliced path integral formulae for a massive vector field accompanied with
a scalar field. Due to the indefinite metric of the Hilbert space upon which we
define field operators, the action appears in the path integral looks quite
different from the classical one. Nevertheless we will find that the effective
action defined by introducing external sources results in the original action.
By taking the effective action as the base of consideration, we study the
proper meaning of the covariance of a path integral.
