PIRSA:14120045

Resurgence in quantum field theory: handling the Devil's invention

APA

Cherman, A. (2014). Resurgence in quantum field theory: handling the Devil's invention. Perimeter Institute for Theoretical Physics. https://pirsa.org/14120045

MLA

Cherman, Aleksey. Resurgence in quantum field theory: handling the Devil's invention. Perimeter Institute for Theoretical Physics, Dec. 09, 2014, https://pirsa.org/14120045

BibTex

          @misc{ scivideos_PIRSA:14120045,
            doi = {10.48660/14120045},
            url = {https://pirsa.org/14120045},
            author = {Cherman, Aleksey},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Resurgence in quantum field theory: handling the Devil{\textquoteright}s invention},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2014},
            month = {dec},
            note = {PIRSA:14120045 see, \url{https://scivideos.org/index.php/pirsa/14120045}}
          }
          

Aleksey Cherman University of Minnesota

Talk numberPIRSA:14120045
Source RepositoryPIRSA

Abstract

Renormalized perturbation theory for QFTs typically produces divergent series, even if the coupling constant is small, because the series coefficients grow factorially at high order. A natural, but historically difficult, challenge has been how to make sense of the asymptotic nature of perturbative series.  In what sense do such series capture the physics of a QFT, even for weak coupling?   I will discuss a recent conjecture that the semiclassical expansion of path integrals for asymptotically free QFTs - that is, perturbation theory - yields well-defined answers once the implications of  resurgence theory are taken into account.   Resurgence theory relates expansions around different saddle points of a path integral to each other, and has the striking practical implication that the high-order divergences of perturbative series encode precise information about the non-perturbative physics of a theory.  These ideas will be discussed in the context of a QCD-like toy model theory, the two-dimensional principal chiral model, where resurgence theory appears to be capable of dealing with the most difficult types of divergences, the renormalons.  Fitting a conjecture by ’t Hooft, understanding the origin of renormalon divergences allows us to see the microscopic origin of the mass gap of the theory in the semiclassical domain.