Speaker
Description
In quantum mechanics and quantum field theory the perturbative series usually have factorially growing coefficients, hence being non-convergent asymptotic expansions. In order to go beyond the approximation given by the optimal truncation one can Borel-resum the series but generically extra contributions (non-perturbative in the coupling) such as instantons, must be included to reproduce the exact results.
I will show that in a class of quantum mechanical problems one can define suitably modified
perturbative expansions which are Borel-resummable to the exact results, avoiding the need to include
instantons. The non-perturbative contributions are therefore encoded in the coefficients of the new
expansions.
I will illustrate this explicitly in examples which are known to contain non-perturbative effects,
such as the (supersymmetric) double-well potential and the perturbative expansion around a false
vacuum. I will comment on possible extensions to quantum field theory.
| Presentation type | Parallel talk |
|---|
