Discovery-HET seminar by Aleksey Cherman – University of Copenhagen

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Discovery-HET seminar by Aleksey Cherman

Resurgence in quantum field theory: dealing with the Devil’s invention

It has been known for more than 60 years that renormalized perturbation theory for QFTs typically produces divergent series,  because the series coefficients grow factorially at high order.  Naive attempts to assign values to such sums produce seemingly-unavoidable ambiguities.   This leads to many questions: In what sense do asymptotic series capture the physics of a QFT, even for weak coupling?  Are semi-classical expansions inherently ambiguous?  Is the only way to rigorously define QFT path integrals via some lattice regulator?  Does perturbation theory know anything quantitative about non-perturbative physics?  How important are these issues in QCD and other QFTs we care about?  I'll review some recent developments showing that much insight into such questions can be obtained by using resurgence theory and Picard-Lefchetz theory.