Editing S-matrix (section)

== Dyson series ==

{{Main article|Dyson series}}

The most widely used expression for the ''S''-matrix is the Dyson series. This expresses the ''S''-matrix operator as the [[Series (mathematics)|series]]:
<math display="block">S = \sum_{n=0}^\infty \frac{(-i)^n}{n!} \int \cdots \int d^4x_1 d^4x_2 \ldots d^4x_n T [ \mathcal{H}_{\rm{int}}(x_1) \mathcal{H}_{\rm{int}}(x_2) \cdots \mathcal{H}_{\rm{int}}(x_n)] </math>
where:
* <math>T[\cdots]</math> denotes [[time-ordering]],
* <math>\; \mathcal{H}_{\rm{int}}(x)</math> denotes the [[interaction Hamiltonian]] density which describes the interactions in the theory.