Hi,
no, in general no explicit representations are used.
I only implemented rules like
MetricTensor[mu,nu] MetricTensor[mu,nu] --> 4
For the Levi-Civita Tensor there is antisymmetry implemented and
things like:
In[6]:= SetOptions[Eps,Dimension->D];
In[7]:= t=LCD[m,n,r,s]//FCI
Out[7]= eps[m, n, r, s]
In[8]:= %//InputForm
Out[8]//InputForm=
Eps[LorentzIndex[m, D], LorentzIndex[n, D], LorentzIndex[r, D],
LorentzIndex[s, D]]
In[9]:= Contract[t t]//Factor2
Out[9]= (1 - D) (2 - D) (3 - D) D
-- The only exception is if you provide integer arguments to Eps, like:In[10]:= Eps[1,2,3,4]
Out[10]= 1
But this should not happen normally.
--
The only place where the metric comes into play is for one-loop calculations, and there in the convention for sign ( p^2 - m^2 ) in the PropagatorDenominator function (and FeynAmpDenominator and alike).
Maybe there are a few more random places where sign convention plays a role; but for normal contraction operations it is irrelevant since everything is just algebra, no components used.
Frederik might want to elaborate more on what conventions he uses in Phi.
Rolf Mertig
On Friday 16 November 2001 05:54 pm, Tim Oppermann wrote: > Hello Everyone, > does anybody know, if one can use Feyncalc in Euclidean space just like > in Minkowski space? Or in different words, do the LeviCevitta Tensor or > the metric tensor have explicit representations when used for > calculations? > We would be happy, if anyone could answer this question or could give us > a hint how to find out. Thank you. > Tim
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