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
Famous quotes containing the words canonical and/or formulation:
“If God bestowed immortality on every man then when he made him, and he made many to whom he never purposed to give his saving grace, what did his Lordship think that God gave any man immortality with purpose only to make him capable of immortal torments? It is a hard saying, and I think cannot piously be believed. I am sure it can never be proved by the canonical Scripture.”
—Thomas Hobbes (1579–1688)
“You do not mean by mystery what a Catholic does. You mean an interesting uncertainty: the uncertainty ceasing interest ceases also.... But a Catholic by mystery means an incomprehensible certainty: without certainty, without formulation there is no interest;... the clearer the formulation the greater the interest.”
—Gerard Manley Hopkins (1844–1889)