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Feynman Diagrams

Graphical representations of particle interactions in QED, depicting virtual particles mediating forces between charged fields. They satisfy specific commutation rules.
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The statement of the theorem

The scattering amplitude M\mathcal{M} for a process involving NN external legs is given by the sum over all connected Feynman diagrams D\mathcal{D}: M=∑D(−1)∣D∣×(Product of propagators)×(Product of vertices)\mathcal{M} = \sum_{\mathcal{D}} (-1)^{|\mathcal{D}|} \times (\text{Product of propagators}) \times (\text{Product of vertices}) where the propagators are defined in momentum space as the inverse of the relevant differential operator (e.g., the photon propagator Dμν(q)=−igμνq2+iϵD_{\mu\nu}(q) = \frac{-i g_{\mu\nu}}{q^2 + i\epsilon}), and the vertices are determined by the interaction Lagrangian.
Source: Wikipedia