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+3 votes

Hello, dear forum users.
Sorry for disturbance.
I wanted to check simple fierz identities using Cadabra.

$$\bar{u}(k_{1}) \gamma^\mu P_L u(p_{1})\bar{v}(p_{2})\gamma_{\mu}P_{L}v(k_{2})$$
where
$$P_L=(1+\gamma^5)/2$$
is a projection operator.

I used the following code. Seemingly the code is missing something as Cadabra gives the result neglecting chirality of \lambda and \chi. What should I add or change to get the correct result, taking chirality into account? The result should be something like:

$$\bar{\nu}_e\gamma^\mu (1+\gamma_5)e\bar{e}\gamma_{\mu}(1+\gamma_5)\nu_e=\bar{e}\gamma^\mu (1+\gamma_5)e\bar{\nu_e}\gamma_{\mu}(1+\gamma_5)\nu_e$$.

{m,n,p#}::Indices; 
{m,n,p}::Integer(0..3); 
\Gamma{#}::GammaMatrix;
\bar{#}::DiracBar; 
\psi::Spinor(dimension=4, type=Weyl); 
\theta::Spinor(dimension=4, type=Weyl); 
\lambda::Spinor(dimension=4, type=Weyl, chirality=Negative); 
\chi::Spinor(dimension=4, type=Weyl, chirality=Negative); 
ex:=\bar{\theta} \Gamma_{m} \chi \bar{\psi} \Gamma^{m} \lambda;
fierz(ex, $\theta, \lambda, \psi, \chi$);
asked in General questions by (150 points)
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1 Answer

0 votes

Do we have any updates on these chiral Fierz identities?

answered by (150 points)
edited by
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