  It is argued that the massive gauge field theory without the Higgs mechanism
can well be set up on the gauge-invariance principle based on the viewpoint
that a massive gauge field must be viewed as a constrained system and the
Lorentz condition, as a constraint, must be introduced from the beginning and
imposed on the Yang-Mills Lagrangian. The quantum theory for the massive gauge
fieldis may perfectly be established by the quantization performed in the
Hamiltonian or the Lagrangian path-integral formalism by means of the Lagrange
undetermined multiplier method and shows good renormalizability and unitarity.
