(Anti)Symmetrized Vertices
Lukong Cornelius Fai · 2019
The Feynman diagrams examined previously in this book treat direct and exchange matrix elements separately. It is simpler and more convenient for many purposes to combine them as a single (anti)symmetrized matrix element. Therefore, we formulate the perturbation theory via the (anti)symmetrized vertex introduced earlier for the residual Hamiltonian U ^ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429196942/b2ea3b11-e25e-4898-8f0e-57a6f2c3a2ac/content/math5_1.tif"/> . For simplicity, we consider the following two-body action functional: 603 S int ψ ^ ∗ , ψ ^ = 1 4 ∑ α 1 α 2 α ′ 1 α ′ 2 α 1 α 2 U ^ α ′ 1 α ′ 2 ∫ 0 β d τ ψ ^ α 1 † τ ψ ^ α 2 † τ ψ ^ α ′ 2 τ ψ ^ α ′ 1 τ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429196942/b2ea3b11-e25e-4898-8f0e-57a6f2c3a2ac/content/math5_2.tif"/>