Hello!
I would like to know if sympy can be used for Quantum Field Theory
calculations. In particular, I would like to compute traces of dirac
matrices and contract them with four-vectors. For example, the
following holds true (latex notation):
Tr ( \gamma^\mu \gamma^\alpha \gamma^\nu \gamma^\beta ) p_\alpha n_
\beta = 4 ( p^\mu n^\nu + n^\mu p^\nu - g^{\mu \nu} p \cdot n )
I am using the following clifford identity to calculate the right hand
side:
\gamma^\mu \gamma^\nu + \gamma^\nu \gamma^\mu = 2 g^{\mu \nu}
\cdot 1
The \gamma^\mu are elements of a clifford algebra and at the same time
are lorentz vectors, g^{\mu \nu} is the metric tensor. Since the
\gamma^\mu are represented by 4x4 matrices, I can take the trace of
them. Because of the identity above and
Tr (1) = 4
I can show that
Tr ( \gamma^\mu \gamma^\nu ) = 4 g^{\mu \nu}
By repeatedly applying the clifford identity I can derive identities
for traces with than two gamma matrices.
Does somebody know if this is possible with sympy? When I looked into
sympy's documentation I noticed there are already modules for tensors
and geometric algebra, but I did not find anything to work out the
traces.
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