Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1993-11-25
Ann.Phys.240:266-314,1995
Physics
Nuclear Physics
Nuclear Theory
50 pages, RevTeX. Major changes from original version. Thirty figures available upon request to phdrp@pippin.cc.flinders.edu.a
Scientific paper
10.1006/aphy.1995.1046
The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor's method which require clarification. Firstly, it is not clear whether Taylor's original method is equivalent to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan and Blankleider (TRAB). Secondly, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor's method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. It then explores how far Taylor's method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor's method, and derives corrections which compensate for this double-counting.
Afnan Iraj R.
Phillips Daniel R.
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