Science / Technology - Colloquium
Monday, April 23, 2007
4:00 PM-5:00 PM
Travel Destination
In quantum field theory, the Dyson scattering matrix is a perturbation expansion in the interaction Hamiltonian that generates an infinite series of Feynman diagrams. A holy grail of QFT is to sum the series. The Bethe-Salpeter equation (BSE) sums all diagrams in what is known as the ladder approximation, but is restricted to elastic scattering processes. As part of my research, I developed a generalized Bethe-Salpeter equation (GBSE) to handle inelastic processes in the ladder approximation. The GBSE, formulated using quantized scalar field theory introduces a systematic method for analyzing families of coupled reactions. A formalism is developed centered around the amplitude matrix M' defined for a given Lagrangian. M' gives the amplitudes of a family of reactions that arise from the Lagrangian. The formalism demonstrates how these amplitudes, to 2nd order, segregate into independent groups of coupled BSEs. A proof is given of the equivalence of the series of ladder diagrams generated by M' and the S-matrix. The GBSE formalism is applied to the coupled BSE (CBSE) of Faassen and Tjon, showing that the CBSE is missing a coupling channel, and in the expansion, under counts ladder diagrams.
Cost: FREE
Sponsored by: WPI Physics Department, Dr. Stephen Jasperson
Suggested Audiences: College
E-mail:
snj@wpi.edu
Phone: 508-831-5392
Last Modified: April 19, 2007 at 2:22 PM
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