Dimensional renormalization in [Formula presented] theory: Ladders and rainbows

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 55, Issue 8, 1997, Pages 5230-5233

  Delbourgo, R ^a   Elliott, D ^a   McAnally, D S ^b  

^a UNIVERSITY OF TASMANIA   (Australia)

^b UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001052593     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.55.5230     Document Type: Article

References (9)

1. R. Delbourgo, A. Kalloniatis, and G. Thompson, Phys. Rev. D54, 5373 (1996).
2. D. Kreimer, Phys. Lett. B354, 111 (1995); D. Kreimer, J. Knot Theory Ramif. (to be published).
3. In Ref. 1, we deduced the Debye expansion of the Bessel function (and a variant of it) by this artifice, adopting a particularly helpful integral representation of Bessel function. In this paper we are obliged to use the Barnes representation as it is the only version which readily generalizes to (Formula presented) hypergeometric functions; the stationary point analysis is completely different now and has been included for that reason.
4. N. G. de Bruijn, Asymptotic Methods in Analysis (North-Holland, Amsterdam, 1958).
5. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
6. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marychev, Integrals and Series (Additional Chapters) (Nauka, Moscow, 1986); see p. 438, Eq. (12) in particular.
7. In this connection, D. Broadhurst and D. Kreimer, Int. J. Mod. Phys. C6, 519 (1995), have investigated the nature of renormalization constants to seven-loop order for (Formula presented) theory and tied them to knot entanglements.
8. D. Kreimer, “On knots in subdivergent diagrams, ” Mainz Report No. MZ-TH//96-31, 1996 (unpublished).
9. S. F. Edwards, Phys. Rev.90, 284 (1953).