Validity of the kink approximation to the tunneling action

Understand

Coleman tunneling in a general scalar potential with two non-degenerate minima is known to have an approximation in terms of a piecewise linear triangular-shaped potential with sharp 'kinks' at the place of the local minima.

• This approximate potential has a regime where the existence of the bounce solution needs the scalar field to 'wait' for some amount of Euclidean time at one of the 'kinks'.
• We discuss under which conditions a kink approximation of locally smooth 'cap' regions provides a good estimate for the bounce action.