Holonomic Systems of Linear Differential Equations and Feynman Integrals

Publications of the Research Institute for Mathematical Sciences

Volumn 12, Issue , 1977, Pages 131-140

  Kashiwara, Masaki ^a   Kawai, Takahiro ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84862518606     PISSN: 00345318     EISSN: None     Source Type: Journal    
DOI: 10.2977/prims/1195196602     Document Type: Article

References (19)

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2. Chandler, C., Some physical region mass shell properties of renormalized Feynman integrals, Commun. math. Phys., 19 (1970), 169-188.
3. Hironaka, H., M. Lejeune, and B. Teissier, Résolution des singularites des espace analytiques complexes. To appear.
4. lagolnitzer, D. and H. P. Stapp, Pole factorization theorem in S-matrix theory. To appear.
5. Kashiwara, M., On the rationality of roots of b-functions. To appear.
6. Kashiwara, M. and T. Kawai, Micro-hyperbolic pseudo-differential operators I, J. Math. Soc. Japan, 27 (1975), 359-404.
7. Kashiwara, M. and T. Kawai, Micro-local properties of [formula omited], Proc. Japan Acad., 51 (1975), 270-272.
8. Kashiwara, M. and T. Kawai, Theory of micro-differential equations, Kōdansha, Tokyo. In preparation.
9. Kashiwara, M., T. Kawai and T. Oshima, Micro-differential equation theoretic approach to Feynman integrals. In preparation.
10. Kashiwara, M., T. Kawai and H. P. Stapp, Micro-analytic structure of the S-matrix and related functions. To appear. A summary is given in this proceeding.
11. Kawai, T. and H. P. Stapp, Micro-local study of the S-matrix singularity structure, Lecture Notes in Physics, No. 39, Springer, Berlin-Heidelberg-New York, pp. 38-48 (1975).
12. Kawai, T. and H. P. Stapp, Discontinuity formula and Sato's conjecture. This proceeding.
13. Landshoff, P. V., D. I. Olive and J. C. Polkinghorne, The hierarchical principle in perturbation theory, Nuovo Cimento 43 (1966), 444-453.
14. Nakanishi, N., Graph Theory and Feynman Integrals. Gordon and Breach, New York-London-Paris (1971).
15. Regge, T., Algebraic topology methods in the theory of Feynman relativistic amplitudes, Report of Battelle Rencontres, Benjamin, New York, pp. 433-458 (1968).
16. Sato, M., Recent development in hyperfunction theory and its application to physics, Lecture Notes in Physics. No. 39, Springer, Berlin-Heidelberg-New York, pp. 13-29 (1975).
17. Sato, M., T. Kawai and M. Kashiwara, Microfunctions and pseudo-differential equations, Lecture Notes in Math. No. 287, Springer, Berlin-Heidelberg-New York, pp. 265-529 (1973).
18. Sato, M., T. Miwa, M. Jimbo and T. Oshima, This proceeding.
19. Speer, E. R., Generalized Feynman Amplitudes, Annals of Mathematics Studies, No. 62, Princeton University Press, Princeton (1969).