On \(p\)-adic aspects of some perturbation series (Q1311516)

A class of perturbation series over the field of rational numbers \(\mathbb{Q}\), containing \(n\)! is considered. Such divergent series (over real or complex number fields) appear usually in perturbative expansion of quantum field theory. It is shown, that such series are convergent in the \(p\)-adic topology. The notion of adelic summability for such series (i.e. when a series converges in the \(p\)-adic topology for all \(p\) and its sum being a rational number independent of \(p\)) is discussed as a possible method of summation of divergent series over \(\mathbb{Q}\) in the topology of real numbers. Possible applications to physical models are discussed.