Feynman Diagram - Canonical Quantization Formulation

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,

S=\sum_{n=0}^{\infty}{i^n\over n!}\int\prod_{j=1}^n d^4 x_j T\prod_{j=1}^n L_v(x_j)\equiv\sum_{n=0}^{\infty}S^{(n)}\;,

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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