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The FORM project for symbolic manipulation of very big expressions
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Dirac algebra in odd spacetime dimensions #547

Open phenomax opened 3 months ago

phenomax commented 3 months ago

Hi,

I am wondering whether FORM is currently able to perform Dirac algebra / traces in odd spacetime dimensions, e.g., $d=2+1$. As written in the manual, tracen works in general dimensions but assumes $d$ to be even. Thus, traces of an odd amount of Gamma Matrices is set to zero, which, unfortunately, no longer holds in $d=2+1$.

Example Code:

#-
off statistics;

v p1;

* Gamma matrices are 2x2 in d=2+1
unittrace 2;

g expr = g_(1,p1,p1,p1);
g expr2 = g_(1,p1,p1);

tracen,1;

print +s;
.end

Is there maybe some functionality that instructs FORM to not apply simplifications specific to even spacetime dimensions?

jodavies commented 3 months ago

As far as I know this is not possible. You would have to implement the algebra yourself, possibly using https://www.nikhef.nl/~form/maindir/documentation/tutorial/online/online.html#SECTION00355000000000000000 for inspiration?