Question
Answer the following about Jean Écalle (“ay-KAHL”)’s theory of resurgent functions, for 10 points each.
[10m] Resurgent functions may solve the divergence of this method in QFT due to factorial growth of the number of terms outpacing exponential decay of coefficients. In quantum mechanics, one form of this method requires rediagonalizing the Hamiltonian in a degenerate subspace.
ANSWER: perturbation theory [or degenerate perturbation theory]
[10h] Specifically, resurgence theory shows that this process can be applied to a divergent perturbative series in a consistent manner. Applying this process can produce singularities in a namesake plane called renormalons.
ANSWER: Borel summation [accept Borel transformation]
[10e] Resurgence theory is particularly useful for asymptotically free theories that are typically impossible to analyze perturbatively, such as this field theory that describes the strong force.
ANSWER: QCD [or quantum chromodynamics]
<Fine, Physics>
Summary
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