Nontrivial homotopy and tunneling by topological instantons

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Abstract
Tunneling by topological instantons is described as a consequence of nontrivial homotopy among field histories and not of barrier penetration. A derivation of the Yang-Mills θ vacua, with finite-action (weak) boundary conditions, is given from this perspective which clarifies certain weaknesses of the barrier-penetration approach. The treatment of nontrivial homotopy in field-theory path integrals is discussed with special attention to the roles of finite action, compactification, continuity of paths, and the justification of the use of Euclidean instantons in a Minkowski-time path integral.

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