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Transcript
Chapter V Interacting Fields Lecture 4 Books Recommended: Lectures on Quantum Field Theory by Ashok Das Advanced Quantum Mechanics by Schwabl Wick’s Theorem Perturbative expansion of S-matrix contains Time ordered product of interaction Hamiltonian. To find transition amplitude one need to find . In the perturbative expansion of S matrix, Those terms will contribute in which Annihilation operator of inital field particle act on the initial state |i>. Time ordering places the operators occurring earlier in time on right of operator occurring later time. Creation operator occurring earlier in time will be placed to right of annihilation operators. This is opposite to normal ordering in which annihilation operators are placed to write of creation operators. Wick’s theorem gives the relation between time ordered product and normal ordered product of the field operators. Consider the case of real scalar field Consider case If and calculate We define contraction for two fields as Which is nothign what definiton of propagtor Thus, we have For complex fields Note In general for a string of fields, we write Example Note Wick’s 1st theorem Wick’s 2nd theorem In above contractions cannot be between the fields within same normal ordered product.
