Canonical Quantization Formulation
Perturbative S-matrix
The probability amplitude for a transition of a quantum system from the initial state to the final state is given by the matrix element
where is the S-matrix.
In the canonical quantum field theory the S-matrix is represented within the interaction picture by the perturbation series in the powers of the interaction Lagrangian,
where is the interaction Lagrangian and signifies the time-ordered product of operators.
A Feynman diagram is a graphical representation of a term in the Wick's expansion of the time-ordered product in the -th order term of the S-matrix,
where signifies the normal-product of the operators and takes care of the possible sign change when commuting the fermionic operators to bring them together for a contraction (a propagator).
Read more about this topic: Feynman Diagram
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