  By using a continuum of oscillators as a reservoir, we present a classical
and a quantum-mechanical treatment for the Higgs model in the presence of
dissipation. In this base, a fully canonical approach is used to quantize the
damped particle on a spherical surface under the action of a conservative
central force, the conjugate momentum is defined and the Hamiltonian is
derived. The equations of motion for the canonical variables and in turn the
Langevin equation are obtained. It is shown that the dynamics of the
dissipative Higgs model is not only determined by a projected susceptibility
tensor that obeys the Kramers-Kronig relations and a noise operator but also
the curvature of the spherical space. Due to the gnomonic projection from the
spherical space to the tangent plane, the projected susceptibility displays
anisotropic character in the tangent plane. To illuminate the effect of
dissipation on the Higgs model, the transition rate between energy levels of
the particle on the sphere is calculated. It is seen that appreciable
probabilities for transition are possible only if the transition and
reservoir's oscillators frequencies to be nearly on resonance.
