Two-component spinor calculations in FeynCalc

[mg18121]

Hello! I am very new to FeynCalc and I am wondering if FeynCalc is suitable for calculations using two-component spinor techniques described arXiv:0812.1594. In particular, I have the following questions:

1. Is it possible to define $\overline{\sigma} = \left(\mathbf{1},-\vec{\sigma}\right)$ in addition to PauliSigma, which is $\sigma = \left(\mathbf{1},\vec{\sigma}\right)$?
2. Is it possible to use FeynCalc to evaluate the traces of the following form (see Eqs. (2.56-2.58) in arXiv:0812.1594):

$\text{Tr}\left[\sigma^\mu \overline{\sigma}^\nu\right] = 2 g^{\mu \nu}$,
$\text{Tr}\left[\sigma^{\mu}\overline{\sigma}^\nu \sigma^\rho \overline{\sigma}^{\kappa}\right] = 2\left(g^{\mu\nu}g^{\rho \kappa} - g^{\mu \rho} g^{\nu \kappa} + g^{\mu \kappa}g^{\nu \rho} + i \epsilon^{\mu\nu\rho\kappa}\right)$?

3. Is it possible to introduce dotted and undotted indecies?

Any clarifications are greatly appreciated!

[vsht]

Hi, the Pauli algebra implemented in FeynCalc is essentially geared towards nonrelativistic calculations rather than SUSY. All the points you mentioned would require quite some changes in the source code. So if you need something that works out-of-the-box, I'm afraid that you need to look for another tool. Cheers, Vlad Am 20.09.23 um 01:06 schrieb mg18121:

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Hello! I am very new to FeynCalc and I am wondering if FeynCalc is suitable for calculations using two-component spinor techniques described arXiv:0812.1594 <https://arxiv.org/abs/0812.1594>. In particular, I have the following questions: 1. Is it possible to define $\overline{\sigma} = \left(\mathbf{1},-\vec{\sigma}\right)$ in addition to PauliSigma, which is $\sigma = \left(\mathbf{1},\vec{\sigma}\right)$? 2. Is it possible to use FeynCalc to evaluate the traces of the following form (see Eqs. (2.56-2.58) in arXiv:0812.1594 <https://arxiv.org/abs/0812.1594>): $\text{Tr}\left[\sigma^\mu \overline{\sigma}^\nu\right] = 2 g^{\mu \nu}$, $\text{Tr}\left[\sigma^{\mu}\overline{\sigma}^\nu \sigma^\rho \overline{\sigma}^{\kappa}\right] = 2\left(g^{\mu\nu}g^{\rho \kappa} - g^{\mu \rho} g^{\nu \kappa} + g^{\mu \kappa}g^{\nu \rho} + i \epsilon^{\mu\nu\rho\kappa}\right)$? 3. Is it possible to introduce dotted and undotted indecies? Any clarifications are greatly appreciated! — Reply to this email directly, view it on GitHub <#232>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABXSD5DPMOQGSDAMSSFJD5DX3IQQVANCNFSM6AAAAAA47AJ5Z4>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[mg18121]

Got it! Thank you!