Schwinger's diagrammatic approach, also known as Feynman diagram technique or perturbation theory, is a powerful method for calculating cross sections and scattering amplitudes in quantum field theory. It was developed by Julian Schwinger and Richard Feynman independently in the 1940s.
In this approach, interactions between particles are represented by Feynman diagrams, which are graphical representations of terms in the perturbative expansion of the scattering amplitude. Each line in the diagram represents a particle or antiparticle, and the vertices represent the interactions between these particles. The lines can be thought of as propagators, indicating the propagation of particles in space and time.
The basic idea is to break down the calculation of a complex scattering process into a series of simpler sub-processes, which can be represented by Feynman diagrams. The scattering amplitude for the full process is then obtained by summing over all possible diagrams contributing to that process. Each diagram represents a particular arrangement of incoming and outgoing particles and the interactions between them.
To calculate the cross section, one squares the absolute value of the scattering amplitude and integrates over the phase space of the final state particles. The cross section provides a measure of the probability for a particular scattering process to occur.
Schwinger's diagrammatic approach allows for a systematic and organized calculation of scattering amplitudes in terms of Feynman diagrams. It provides a visual representation of the underlying physics and simplifies complex calculations by breaking them down into manageable parts. The technique has been widely used in quantum field theory to compute scattering processes and make predictions that can be compared with experimental results.
It is worth noting that Schwinger's diagrammatic approach is a perturbative technique and is most applicable in situations where the interactions are weak. For strongly interacting systems, other non-perturbative methods, such as lattice QCD, become necessary.