Department of Physics, Jilin University,

Changchun 130023, P. R. CHINA

E-mail: junchens@public.cc.jl.cn

**Massive gauge field theory without Higgs mechanism**

**Abstract:**

It has been shown that the massive non-Abelian gauge field theory in
which all the gauge fields have the same mass may really be set up on the
gauge-invariance principle without the help of the Higgs mechanism. The
essential points of achieving this conclusion are : (1) The massive gauge
field must be viewed as a constrained system in the whole space of vector
potential. Therefore, the Lorentz condition, as a necessary constraint,
must be introduced from the onset and imposed on the massive Yang-Mills
Lagrangian so as to restrict the unphysical degrees of freedom involved
in the Lagrangian. That is to say, the massive Yang-Mills Lagrangian itself
is not complete to describe the dynamics of the massive gauge field; (2)
The gauge-invariance of gauge field dynamics should be more generally required
to the action of the field other than the Lagrangian because the action
is of more fundamental dynamical meaning. In particular, the gauge-invariance
for the constrained system should be required to the action written in
the physical subspace defined by the Lorentz condition in which the fields
exist and move only; (3) In the physical subspace , only the infinitesimal
gauge transformations are possible to exist and necessary to be considered
in inspection of whether the theory is gauge-invariant or not; (4) To construct
a correct gauge field theory, the residual gauge degrees of freedom existing
in the physical subspace must be eliminated by the constraint condition
on the gauge group. This constraint condition may be determined by requiring
the action to be gauge-invariant. Thus, the theory is set up from beginning
to end on the gauge-invariance principle. These points which are not realized
clearly in the past are important to build up a correct quantum massive
non-Abelian gauge field theory. The quantization of the theory can well
be performed in the Hamiltonian path-integral formalism or in the
Lagrangian path-integral formalism. To achieve a Lorentz-covariant quantization,
it is necessary to incorporate the Lorentz condition into the massive Yang-Mills
Lagrangian so that each component of a vector potential acquires a canonically
conjugate counterpart. This makes the Lorentz-covariant formulation of
the Hamiltonian path-integral quantization become possible. The result
of this quantization is confirmed by the quantization carried out
in the Lagrangian path-integral formalism by means of the Lagrange
undetermined multiplier method. The latter method of quantization is proposed
first and proved to be equivalent to the Faddeev-Popov approach.
The renormalizability and unitarity of the theory has also been exactly
proved to be no problems.