Re: Integrating Feynman integrals in mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg50874] Re: Integrating Feynman integrals in mathematica
- From: pabird at supanet.com (Xman)
- Date: Sat, 25 Sep 2004 01:55:15 -0400 (EDT)
- References: <firstname.lastname@example.org> <email@example.com>
- Sender: owner-wri-mathgroup at wolfram.com
"Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk> wrote in message news:<cj0n33$lc6$1 at smc.vnet.net>... > Unless I have missed the point of your question, this is standard material > covered in textbooks on quantum field theory. I have Itzykson + Zuber's > tome, and I find your first integral discussed in section 1-3-1 on Green > functions. Your second integral is related to your first integral by the > trick of differentiating w.r.t. an auxiliary parameter (i.e. make the > replacement m^2-->a m^2 in your first integral, differentiate w.r.t. a, then > set a-->1). > Thanks for your input. Yes, the integrals are from QFT but the books on QFT I have read usually leave the integrals as they are or give an approximation to them only. So I want to find a *simple* series solution to them which I believe is simplest in the form above. I am sure I have seen something similar somewhere before unsfortunately can't remember where! I was hoping that someone more knowledgable in Mathematica or QFT than me would be able to confirm what I susupect which is that the second integral can be written as: Sum[ ((m^2/4)^n |x.x|^n / n!^2)*( log|x.x| - Sum[1/p ,p=1..n]) ,n=0..Infinity] From which, for example, I can instantly see the function is smooth and not wave-like. Such a series would also, it seems, converge very rapidly and accuratley which would be very useful. I also believe that in the form P(m|x|)log(|x|)-Q(m|x|), the function P is the BesselI[0,x] function from Mathematica but I don't know whether Q is a well-known function.