23.3. Instantons Instantons are finite action classical solutions of Euclidean equations of motion and are closely related to tunnelling phenomena among degenerate vacua. Consider a unit-mass particle in one dimension, under the potential V(q) = 1−cosq.

a. Write down the Euclidean action of this problem and the corresponding equation of motion.

b. Show that the finite-action solutions of the Euclidean equation of motion are the same as the finite-energy static solitons of the Sine–Gordon model.