Instantons

Abstract

We have seen that several quantities in quantum field theory can be expressed in terms of functional integrals whose integrands contain either exp(iS), where S is the action integral, or exp(−S eucl), where S eucl is the Euclidean action integral. For the approximate evaluation of these integrals, one can use the stationary-phase method in the first case, and the Laplace method in the second. The application of these methods can be seen as an application of the semiclassical approximation. Indeed, if we momentarily abandon our convention that ħ = 1, so the exponentials involve iħ −1 S and ħ −1 S eucl instead of iS or Seucl, we can establish the asymptotic behavior as ħ → 0 by applying the stationary-phase method or the Laplace method.KeywordsGauge TheoryGauge FieldHomotopy ClassTopological ChargeEuclidean ActionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.