Name: Lingxiao Xu Date: 11/26/14-05:34:58 AM Z
Hi,
Thanks for attention.
Here is one of my results which cantains Levi-Civita tensor contracted
with four-momentums,
1/(8 s t
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\))
g^4 sw^2 (s^2 t^2 - t^4 + s^2 t u + t^3 u + t^2 u^2 - t u^3 -
8 s^2 t
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) + 4 s
t^2
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) - 4
s^2 u
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) - 4 s
t u
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) - 4
t^2 u
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) + 4
u^3
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) +
8 I t Eps[Momentum[p1], Momentum[p2],
Momentum[-p1 - p2 - p3],
Momentum[p3]]
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) +
8 I t Eps[Momentum[p1], Momentum[p2],
Momentum[p3],
Momentum[p3 - p4]]
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) +
8 I t Eps[Momentum[p1], Momentum[p3],
Momentum[p4],
Momentum[p1 + p2 + p4]]
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) + 12
s^2
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) + 16
s t
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) - 12
t^2
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) + 16
s u
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) + 8 t
u
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) - 12
u^2
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) -
16 I Eps[Momentum[p1], Momentum[p2],
Momentum[-p1 - p2 - p3],
Momentum[p3]]
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) +
8 I Eps[Momentum[p1], Momentum[p2],
Momentum[p3],
Momentum[p3 - p4]]
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) +
8 I Eps[Momentum[p1], Momentum[p2],
Momentum[p3],
Momentum[p1 + p2 + p4]]
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) -
8 I Eps[Momentum[p1], Momentum[p3],
Momentum[p4],
Momentum[p1 + p2 + p4]]
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\) - 56
s
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(6\)]\) + 24
t
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(6\)]\) + 8
u
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(6\)]\) -
16
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(8\)]\) -
4 I (s - t - u) Eps[Momentum[p1], Momentum[p2],
Momentum[p3],
Momentum[p4]] (t - 2
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\)) +
4 I Eps[Momentum[p1], Momentum[p2],
Momentum[p3 - p4],
Momentum[p4]] (s t - 2 (s + t + u)
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(2\)]\) + 6
\!\(\*SubsuperscriptBox[\(m\), \(W\), \(4\)]\)))
So in this kind of condition, how can I simplify the Levi-Civita tensor further?
Best Regards!
Lingxiao