Question

Are Instantons Quantum or Classical?

Answer 1

An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instantonis a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory.

Answer 2

Instantons are solutios of the Euclidean version of the theory (QFT or QM) and describe certain types of tunneling processes. For thus reason they are proper of quantum theories where both the Euclidean version and quantum tunnelling make sense. Their use in quantum theory is based on the so-called saddle point method which permits to compute an estimation of Euclidean path integral using Euclidean classical solutions of Euler-Lagrange solutions. However these solurions have no proper classical meaning as they describe evolutions which are not classically permitted.