Coleman's Instanton and Level Splitting in Double Well

[lingf]

i am now reading the book by coleman, aspects of symmetry.

i am a bit interested in the instanton.

in his book, he discussed how to calculate the level splitting in a double well potential.

as for this splitting, it seems that he did not give an explicit expression of the coefficient K,

see his equation (2.41) on page 276.

how to calculate the fraction involving det?

 

[blechman]

i believe he does it in the appendix of those notes. but when generalizing to the full QFT, calculating that determinant is VERY difficult, and is almost never done in practice (it is usually enough that we can estimate its size without actually working out the exact value). it was done first (to my knowledge) by 't Hooft in a famous, and very dense, paper.