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Do anyone know if we could do Dirac Gamma Matrix Algebra by FeynCalc with Gamma Matrices defined in different dimension than 4, e.g. DiracTrace of gamma matrices in 2+1 dimension?

Thanks!

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  • $\begingroup$ In the documentation i see the command Dimension. So can't you set the Dimension to 'n' and then define your metric tensor and work with it. $\endgroup$
    – Hubble07
    Sep 22, 2014 at 8:32
  • $\begingroup$ Hi, to make it more specific. Say we have Dirac Gamma matrices in 2+1 d, which are just 2 by 2 Pauli Matrices. the trace of product of three gamma matrices should give me a Levi-Civita in that spacetime dimension. But I could not get the trace correct in FeynCalc. $\endgroup$
    – physicsqiqi0805
    Sep 22, 2014 at 19:53
  • $\begingroup$ Related: Dirac Matrices in Higher Dimensions (Wolfram Demo) $\endgroup$
    – Jens
    Sep 23, 2014 at 0:23

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Sure, e.g.:

TR[DiracMatrix[mu,nu,rho,si,rho,nu,mu,si, Dimension -> n]]

gives 

-4*(-2 + n)^3*n
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  • $\begingroup$ Hi,What I mean is define gamma matrices in different dimensions, say in 2+1-d, gamma matrices are just Pauli Matrices, and trace of three gamma matrices should give you Levi-Civita \epsilon_{\mu \nu \sigma}. I do not know how it works. It seems like Levi-Civita are not available in (2+1)-d. $\endgroup$
    – physicsqiqi0805
    Sep 22, 2014 at 14:22

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