Massive Gauge Bosons in Yang-Mills Theory without Higgs Mechanism

Two kinds of Yang-Mills fields are found upon the concepts of mass eigenstate and nonmass eigenstate. The Yang-Mills fields of the first kind were proposed by Yang and Mills, which couple to the mass eigenstates with the same rest mass, whose gauge bosons are massless. I find that there are second kind of Yang-Mills fields, which are constructed on a five-dimensional manifold. Only the nonmass eigenstates couple to the Yang-Mills fields of the second kind, which are the nonmass eigenstates as well and composed of mass eigenstates of gauge bosons. The mass eigenstates of the Yang-Mills fields of the second kind live in the four-dimensional spacetime, the corresponding gauge bosons of which may be massive. The SU(2)\times U(1) gauge fields of the second kind are studied carefully, whose gauge bosons, which are the mass eigenstates, are the W^{\pm}, Z^{0} and photon fields. The rest masses of W^{\pm} and Z^{0} obtained are the same as that given by the Glashow-Salam-Weinberg model of electroweak interactions. It is discussed that this model should be renormalizable.