Open AccessA Construction of an Effective Hamiltonian from Feynman Diagrams
Author(s) -
Yuki Yamamoto
Publication year - 2001
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp.106.99
Subject(s) - feynman diagram , physics , hamiltonian (control theory) , renormalization , covariant transformation , coupling constant , mathematical physics , yukawa potential , propagator , renormalization group , theoretical physics , quantum mechanics , mathematics , mathematical optimization
We study a similarity transformation to construct an effective Hamiltoniansystematically, which does not contain particle-number-changing interactions,by means of Fukuda-Sawada-Taketani-Okubo's method. We show that suchHamiltonian can be constructed from Feynman diagrams and give rules forconstructing it in the Light-Front Yukawa model. We prove that it isrenormalized by the familiar covariant perturbative renormalization procedure.It is very advantageous that the effective Hamiltonian can be obtained from ourrules {\em immediately}. We also numerically diagonalize it to the second orderin the coupling constant as an exercise.Comment: 32 pages, 22 figures, PTPTe
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