Alien Calculus and non perturbative effects in Quantum Field Theory

Understand

In many domains of physics, methods are needed to deal with non-perturbative aspects.

• I want here to argue that a good approach is to work on the Borel transforms of the quantities of interest, the singularities of which give non-perturbative contributions.
• These singularities in many cases can be largely determined by using the alien calculus developed by Jean \'Ecalle.
• My main example will be the two point function of a massless theory given as a solution of a renormalization group equation.