Abstract:
Perturbative methods are worth trying whenever, to find exact solution, one is forced to neglect some interesting effects. Needless to say, such situations are met almost everywhere in physics. Conditions for a successful application of perturbative methods. Traditional shape of perturbative methods in quantum theory. Divergent perturbative series and their physical value. What one should know about the physics of a problem to apply perturbation theory. Asymptotic series, regular and analytic summation methods. In what sense a power series loses physical information. Uniqueness theorems. Borel summation and its generalizations. Alternative expansions, better adapted to the physics of the problem. Use of optimal conformal mapping and Pade approximants. Enhancement of convergence rate. Non-power series. Replacing a series with an integral. Form of optimal expansion functions when some a priori information about the expanded function is known. Stepping out of perturbation theory?