Using the Hopf algebra structure of QFT in calculations

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 60, Issue 10, 1999, Pages

  Delbourgo, R ^b  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

^b UNIVERSITY OF TASMANIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18144402422     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.60.105025     Document Type: Article

References (23)

1. N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed. (Wiley, New York, 1980)
2. K. Hepp, Commun. Math. Phys. 2, 301 (1966)
3. Commun. Math. Phys.W. Zimmermann, 15, 208 (1969).
4. D. Kreimer, Adv. Theor. Math. Phys. 2.2, 303 (1998).
5. A. Connes and D. Kreimer, Commun. Math. Phys. 199, 203 (1998).
6. D. Kreimer, Commun. Math. Phys. 204, 669 (1999).
7. D.J. Broadhurst and D. Kreimer, J. Symb. Comput. 27, 581 (1999).
8. D. Kreimer, “Chen’s Iterated Integral Represents the Operator Product Expansion,” hep-th/9901099.
9. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations (Wiley, New York, 1987).
10. G. ’t Hooft, Nucl. Phys. B538, 389 (1999).
11. S. Weinberg, The Quantum Theory of Fields (Cambridge University Press, Cambridge, England, 1994), Vols. I and II.
12. D. Kreimer, J. Knot Th. Ram. 6, 479 (1997).
13. R. Delbourgo, A.C. Kalloniatis, and G. Thompson, Phys. Rev. D 54, 5373 (1996).
14. R Delbourgo, D. Elliott, and D.S. McAnally, Phys. Rev. D 55, 5230 (1997).
15. D.J. Broadhurst, R. Delbourgo, and D. Kreimer, Phys. Lett. B 366, 421 (1996).
16. T.K. Chen, Bull. Am. Math. Soc. 83, 831 (1977).
17. C. Kassel, Quantum Groups (Springer, Berlin, 1995);S. Shnider and S. Sternberg, Quantum Groups (International Press, 1993).
18. A. Davydychev and R. Delbourgo, J. Math. Phys. 39, 4299 (1998).
19. J.M. Borwein and D.J. Broadhurst, “Determination of Rational Dedekind Zeta Invariants of Hyperbolic Manifolds and Feynman Knots and Links,” hep-th/9811173.
20. D.J. Broadhurst and D. Kreimer, Int. J. Mod. Phys. C 6, 519 (1995).
21. D.J. Broadhurst, J. Gracey, and D. Kreimer, Z. Phys. C 75, 559 (1997).
22. D.J. Broadhurst and D. Kreimer, Phys. Lett. B 393, 403 (1997).
23. J.C. Collins, Renormalization (Cambridge University Press, Cambridge, England, 1984).