  We investigate a polyacetylene ring in an axially symmetric, static electric
field with a modified SSH Hamiltonian of a polyacetylene chain. An effective
gauge potential of the single electron Hamiltonian due to spin-field
interaction is obtained and it results in a Fr\"{o}hlich's type of
superconductivity equivalent to the effect of travelling lattice wave. The
total energy as well as the persistent current density are shown to be a
periodic function of the flux of the gauge field embraced by the polyacetylene
ring.
