dorsal/arxiv
View SchemaThe classification of diagrams in perturbation theory
| Authors | D. R. Phillips, I. R. Afnan |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9311029 |
| URL | https://arxiv.org/abs/nucl-th/9311029 |
| DOI | 10.1006/aphy.1995.1046 |
| Journal | Ann.Phys.240:266-314,1995 |
Abstract
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.
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"abstract": "The derivation of scattering equations connecting the amplitudes obtained\nfrom diagrammatic expansions is of interest in many branches of physics. One\nmethod for deriving such equations is the classification-of-diagrams technique\nof Taylor. However, as we shall explain in this paper, there are certain points\nof Taylor\u0027s method which require clarification. Firstly, it is not clear\nwhether Taylor\u0027s original method is equivalent to the simpler\nclassification-of-diagrams scheme used by Thomas, Rinat, Afnan and Blankleider\n(TRAB). Secondly, when the Taylor method is applied to certain problems in a\ntime-dependent perturbation theory it leads to the over-counting of some\ndiagrams. This paper first restates Taylor\u0027s method, in the process uncovering\nreasons why certain diagrams might be double-counted in the Taylor method. It\nthen explores how far Taylor\u0027s method is equivalent to the simpler TRAB method.\nFinally, it examines precisely why the double-counting occurs in Taylor\u0027s\nmethod, and derives corrections which compensate for this double-counting.",
"arxiv_id": "nucl-th/9311029",
"authors": [
"D. R. Phillips",
"I. R. Afnan"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1006/aphy.1995.1046",
"journal_ref": "Ann.Phys.240:266-314,1995",
"title": "The classification of diagrams in perturbation theory",
"url": "https://arxiv.org/abs/nucl-th/9311029"
},
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