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A study of Feynman integrals by micro-differential equations |
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| Authors: | Masaki Kashiwara Takahiro Kawai Toshio Oshima |
| Institution: | (1) Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA;(2) Department of Mathematics, Harvard University, Cambridge, MA, USA;(3) Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan;(4) Department of Mathematics, College of General Education, University of Tokyo, Tokyo, Japan |
| Abstract: | We use the holonomic character of Feynman integrals to describe their singularity structure explicitly in some simple cases. The results in §1 show that under moderate conditions Feynman amplitudes can be locally expressed essentially in terms of Legendre functions near the points where two positive- Landau-Nakanishi surfaces meet. Related topics such as hierarchical principle in perturbation theory are also discussed in terms of holonomic systems involved. In §4 we use the concrete expressions for Feynman amplitudes obtained in §1 to discuss the validity of Sato's conjecture.Supported in part by NSF MCS 75-2333Supported in part by NSF GP 36269 |
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