  According to the conventional concept of the gauge field theory, the local
gauge invariance excludes the possibility of giving a mass to the gauge boson
without resorting to the Higgs mechanism because the Lagrangian constructed by
adding a mass term to the Yang-Mills Lagrangian is not only
gauge-non-invariant, but also unrenormalizable. On the contrary, we argue that
the principle of gauge invariance actually allows a mass term to enter the
Lagrangian if the Lorentz constraint condition is taken into account at the
same time. The Lorentz condition, which implies vanishing of the unphysical
longitudinal field, defines a gauge-invariant physical space for the massive
gauge field. The quantum massive gauge field theory without Higgs mechanism may
well be established by using a BRST-invariant action which is constructed by
the Lagrange undetermined multiplier procedure of incorporating the Lorentz
condition and another condition constraining the gauge group into the original
massive Yang-Mills action. The quantum theory established in this way shows
good renormalizability.
