QUANTUM-MECHANICAL TUNNELING AT FINITE-ENERGY AND ITS EQUIVALENT AMPLITUDES IN THE (VACUUM) INSTANTON APPROXIMATION

The transition amplitude for quantum tunnelling between neighbouring v acua of the sine-Gordon potential at finite energy is estimated with t he help of the path-integral method. The tunnelling process is dominat ed by nonvacuum (periodic) instanton configurations. It is explicitly shown that the amplitude for tunnelling between the nth excited states which is dominated by nonvacuum instantons is equivalent to that of t he vacuum instanton approximation calculated with the 2n-point euclide an Green's function, which is the standard calculation of instanton-li ke transitions in high energy collisions. The equivalence, however, is valid only in the low energy limit, whereas the amplitude for quantum tunnelling with nonvacuum instantons is valid for energies up to the sphaleron mass.