We present a concise review of the recent development of relativistic hydrodynamics and its
applications to heavy-ion collisions. Theoretical progress on the extended formulation of …

The computation of observables in general interacting theories, be them quantum
mechanical, field, gauge or string theories, is a non-trivial problem which in many cases can …

We illustrate the physical significance and mathematical origin of resurgent trans-series
expansions for energy eigenvalues in quantum mechanical problems with degenerate …

A bstract In theories with renormalons the perturbative series is factorially divergent even
after restricting to a given order in 1/N, making the 1/N expansion a natural testing ground for …

A bstract We derive a system of TBA equations governing the exact WKB periods in one-
dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations …

Expansions of physical functions are controlled by their singularities, which have special
structure because they themselves are physical, corresponding to instantons, caustics or …

We consider specific quantum mechanical model problems for which perturbation theory
fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if …

In a wide range of quantum theoretical settings—from quantum mechanics to quantum field
theory, from gauge theory to string theory—singularities in the complex Borel plane, usually …

This highly pedagogical textbook for graduate students in particle, theoretical and
mathematical physics, explores advanced topics of quantum field theory. Clearly divided into …

A bstract A general quantum mechanical or quantum field theoretical system in the path
integral formulation has both real and complex saddles (instantons and ghost-instantons) …