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Question: metrics, scalar product

Question:metrics, scalar product

illuminates 65 Maple 2016
physics trace
November 20 2016
0

Dear Friends, I work with physics paсkage. I have a quation. I don't understend how one works with metrics. For example, let:

with(Physics);
Setup(mathematicalnotation = true);
                 [mathematicalnotation = true]
Setup(spaceindices = uppercaselatin);
                [spaceindices = uppercaselatin]
Define(k, n);
             Defined objects with tensor properties
{k, n, Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu],
  Physics:-g_[mu, nu], Physics:-KroneckerDelta[mu, nu],
  Physics:-LeviCivita[alpha, beta, mu, nu]}
Simplify(k[mu]*g_[mu, nu]);
                             k[nu]
Nice!
Simplify(n[A]*g_[A, B]);
                              n[B]
Very good!

Simplify(n[A]*gamma_[A, B]);
                       n[A] gamma_[A, B]
1) It doesn't work. Why? (I want exactly gamma_[A,B], rather than g_[A,B], because as i guess gamma_[A,B] has a signature [1,1,1] but g_[A,B] has a signature [-1,-1,-1])

 2) And how may I see what is matrices g_[A, B], gamma_[A, B] explicitly? That is I know how to see what is g_[mu, nu], for this one needs write "g_[];".  But how may I see g_[A, B] and gamma_[A, B] in explicitly forms?

3) Why command Trace(g_[mu, nu]))  does not work?"
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