Improved Epstein-Glaser renormalization in coordinate space I. Euclidean framework

Mathematical Physics Analysis and Geometry

Volumn 6, Issue 1, 2003, Pages 59-88

  Gracia Bondía, José M ^a,b,c  

^a BIELEFELD UNIVERSITY   (Germany)

^b UNIVERSITY OF ZARAGOZA   (Spain)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Epstein Glaser renormalization; Scaling

Indexed keywords

EID: 0242524861     PISSN: 13850172     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022414224858     Document Type: Article

References (59)

1. Gracia-Bondía, J. M. and Lazzarini, S.: Improved Epstein-Glaser renormalization in coordinate space II. Lorentz invariant framework, in preparation.
2. Gracia-Bondía, J. M.: Improved Epstein-Glaser renormalization in coordinate space III. The Hopf algebra of Feynman graphs, in preparation.
3. Kreimer, D.: Adv. Theor. Math. Phys. 2 (1998), 303.
4. Connes, A. and Kreimer, D.: Comm. Math. Phys. 210 (2000), 249.
5. Connes, A. and Kreimer, D.: Comm. Math. Phys. 216 (2001), 215.
6. 't Hooft, G. and Veltman, M.: Nuclear Phys. B 44 (1972), 189.
7. Bollini, C. G. and Giambiagi, J. J.: Nuovo Cimento B 12 (1972), 20.
8. Epstein, H. and Glaser, V.: Ann. Inst. Henri Poincaré A 19 (1973), 211.
9. Veltman, M.: Diagrammatica, Cambridge Univ. Press, Cambridge, 1994.
10. Collins, J. C.: Renormalization, Cambridge Univ. Press, Cambridge, 1984.
11. Dosch, H. G. and Müller, V. F.: Fortschr. Phys. 23 (1975), 661.
12. Bellissard, J.: Comm. Math. Phys. 41 (1975), 235.
13. Gracia-Bondía, J. M.: Phys. Lett. B 482 (2000), 315.
14. Brunetti, R. and Fredenhagen, K.: Comm. Math. Phys. 208 (2000), 623.
15. Itzykson, C. and Zuber, J.-B.: Quantum Field Theory, McGraw-Hill, New York, 1980.
16. Stora, R.: Lagrangian field theory, In: C. DeWitt-Morette and C. Itzykson (eds), Proc. Les Houches School, Gordon and Breach, New York, 1973.
17. Popineau, G. and Stora, R.: A pedagogical remark on the main theorem of perturbative renormalization theory, Unpublished preprint, CPT & LAPP-TH (1982).
18. Stora, R.: A note on elliptic perturbative renormalization on a compact manifold, Unpublished undated preprint, LAPP-TH.
19. Pinter, G.: Ann. Phys. 8 10 (2001), 333.
20. 4 theory and the action principle, Doktorarbeit, DESY, 2000.
21. Gracia-Bondía, J. M. and Lazzarini, S.: Connes-Kreimer-Epstein- Glaser renormalization, hep-th/0006106.
22. Güttinger, W.: Phys. Rev. 89 (1953), 1004.
23. Bogoliubov, N. N. and Parasiuk, O. S.: Acta Math. 97 (1957), 227.
24. Freedman, D. Z., Johnson, K. and Latorre, J. I.: Nuclear Phys. B 371 (1992), 353.
25. Schnetz, O.: J. Math. Phys. 38 (1997), 738.
26. Estrada, R., Gracia-Bondía, J. M. and Várilly, J. C.: Comm. Math. Phys. 191 (1998), 219.
27. Estrada, R.: Proc. Roy. Soc. London A 454 (1998), 2425.
28. Estrada, R. and Kanwal, R. P.: A Distributional Approach to Asymptotics, Theory and Applications (2nd edn), Birkhäuser, Boston, 2002.
29. Prange, D.: J. Phys. A 32 (1999), 2225.
30. Steinmann, O.: Perturbation Expansions in Axiomatic Field Theory, Lecture Notes in Phys. 11, Springer, Berlin, 1971.
31. Estrada, R.: Internat. J. Math. and Math. Sci. 21 (1998), 625.
32. Gracia-Bondía, J. M., Várilly, J. C. and Figueroa, H.: Elements of Noncommutative Geometry, Birkhäuser, Boston, 2001.
33. Smirnov, V. A. and Zavialov, O. I.: Theoret. and Math. Phys. 96 (1993), 974.
34. Gelfand, I. M. and Shilov, G. E.: Generalized Functions I, Academic Press, New York, 1964.
35. Kuznetsov, A. N., Tkachov, F. V. and Vlasov, V. V.: Techniques of distributions in perturbative quantum field theory I, hep-th/9612037, Moscow, 1996.
36. Grigore, D. R.: Ann. Phys. (Leipzig) 10 (2001), 473.
37. Kreimer, D.: Knots and Feynman Diagrams, Cambridge Univ. Press, Cambridge, 2000.
38. Andrews, G. E., Askey, R. and Roy, R.: Special Functions, Cambridge Univ. Press, Cambridge, 1999.
39. Chetyrkin, K. G., Kataev, A. L. and Tkachov, F. V.: Nuclear Phys. B 174 (1980), 345.
40. Blanchard, Ph. and Brüning, E.: Generalized Functions, Hilbert Spaces and Variational Methods, Birkhäuser, Basel, 2002.
41. Hörmander, L.: The Analysis of Partial Differential Operators I, Springer, Berlin, 1983.
42. Graham, R. L., Knuth, D. E. and Patashnik, O.: Concrete Mathematics, Addison-Wesley, Reading, MA, 1989.
43. Estrada, R. and Kanwal, R. P.: Proc. Roy. Soc. London A 401 (1985), 281.
44. Estrada, R. and Kanwal, R. P.: J. Math. Anal. Appl. 141 (1989), 195.
45. Blanchet, L. and Faye, G.: gr-qc/0004008, Meudon, 2000.
46. Scharf, G.: Finite Quantum Electrodynamics: the Causal Approach, Springer, Berlin, 1995.
47. Kreimer, D.: Talks at Abdus Salam ICTP, Trieste, March 27, 2001 and Mathematical Sciences Research Institute, Berkeley, April 25, 2001.
48. Gross, D. J.: Applications of the renormalization group to high-energy physics, In: R. Balian and J. Zinn-Justin (eds), Proc. Les Houches School, North-Holland, Amsterdam, 1976.
49. del Aguila, F. and Pérez-Victoria, M.: Acta Phys. Polon. B 28 (1997), 2279.
50. Smirnov, V. A.: Nuclear Phys. B 427 (1994), 325.
51. Dunne, G. V. and Rius, N.: Phys. Lett. B 293 (1992), 367.
52. Gracia-Bondía, J. M.: Modern Phys. Lett. A 16 (2001), 281.
53. Lowenstein, J. H. and Zimmermann, W.: Nuclear Phys. B 86 (1975), 77.
54. Zavialov, O. I.: Theoret. and Math. Phys. 98 (1994), 377.
55. Smirnov, V. A.: Theoret. and Math. Phys. 108 (1997), 953.
56. Haagensen, P. E. and Latorre, J. L.: Phys. Lett. B 283 (1992), 293.
57. Hollands, S. and Wald, R. M.: gr-qc/0111108, Chicago, 2001; Comm. Math. Phys., in press.
58. Hollands, S. and Wald, R. M.: gr-qc/0209029, Chicago, 2002.
59. Brunetti, R., Fredenhagen, K. and Verch, R.: math-ph/0112041, Hamburg, 2001.