  The quantization of the SU(2)$\times $U(1) gauge-symmetric electroweak theory
is performed in the Hamiltonian path-integral formalism. In this quantization,
we start from the Lagrangian given in the unitary gauge in which the unphysical
Goldstone fields are absent, but the unphysical longitudinal components of the
gauge fields still exist. In order to eliminate the longitudinal components, it
is necessary to introduce the Lorentz gauge conditions as constraints. These
constraints may be incorporated into the Lagrangian by the Lagrange
undetermined multiplier method. In this way, it is found that every component
of a four-dimensional vector potential has a conjugate counterpart. Thus, a
Lorentz-covariant quantization in the Hamiltonian path-integral formalism can
be well accomplished and leads to a result which is the same as given by the
Faddeev-Popov approach of quantization.
