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MathGroup Archive 1997

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Mathematica in Quantum Field Theory (II)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7557] Mathematica in Quantum Field Theory (II)
  • From: umino at sbhep.physics.sunysb.edu
  • Date: Fri, 13 Jun 1997 19:38:10 -0400 (EDT)
  • Organization: High Energy Physics, SUNY at Stony Brook
  • Sender: owner-wri-mathgroup at wolfram.com

How do you tell Mathmatica to do the following integral involving delta functions?
(I have to write the integral in LaTeX form)

\int d^4p_1 d^4p_2 d^4p_3 d^4p_4 d^4p_5
\delta^4(k_1 - p_1 - p_2 - p_3) \delta^4(k_2 - p_4 - p_5) 
\delta^3( \vec{p_4} + \vec{p_3} ) \delta(p_1^0 - x_1) \delta(p_2^0 - x_2)
\delta(p_3^0 + x_3) \delta(p_4^0 - x_4) \delta(p_5^0 - x_5)
f(p_1^\mu,p_2^\mu,p_3^\mu,p_4^\mu,p_5^\mu)

This integral is a product involving five one dimmensional, one three dimensional
and two four dimensional delta functions and p_1^\mu = (p_1^0,\vec{p_1}), etc.
It is trivial to do this by hand. The problem is that this is just one term
in a series containing several thousand terms with different functional
dependencies on the delta functions. For example, another term might have
a four dimensional integral that looks like

\delta^4(k_1 - p_1 - p_4 - p_5) \delta^4(k_2 - p_2 - p_3)

I would like to evaluate the entire series simultaneously.

Thanks,

Mathematica challenged


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