Levi-Civita symbol product identity

[ElJefeDelDesierto]

Hello great FeynCalc team.

There exists an identity relating the product of two Levi-Civita symbols (with no contracted indices) to the determinant of a matrix made of metric tensors. The identity is the following

The same identity is shown in Wikipedia. I have proven that this identity holds component by component (by using a python code). My question is: Is it possible to ask FeynCalc to use this identity to replace the product of Levi-Civita symbols in an expression? If so, how?

Thanks in advance!

[vsht]

Hi, Contract does that automatically https://feyncalc.github.io/FeynCalcBookDev/Contract.html Am 20.12.24 um 03:51 schrieb ElJefeDelDesierto:

…

Hello great FeynCalc team. There exists an identity relating the product of two Levi-Civita symbols (with no contracted indices) to the determinant of a matrix made of metric tensors. The identity is the following epsilonepsilonidentity.png (view on web) <https://github.com/user- attachments/assets/12dba086-0cc7-4ac6-8a98-259cf559d737> The same identity is shown in Wikipedia <https://en.wikipedia.org/wiki/ Levi-Civita_symbol>. I have proven that this identity holds component by component (by using a python code). My question is: Is it possible to ask FeynCalc to use this identity to replace the product of Levi-Civita symbols in an expression? If so, how? Thanks in advance! — Reply to this email directly, view it on GitHub <https://github.com/ FeynCalc/feyncalc#291>, or unsubscribe <https://github.com/ notifications/unsubscribe-auth/ ABXSD5HIFOMDUDPVHDYJR4L2GOA3FAVCNFSM6AAAAABT6IHOA6VHI2DSMVQWIX3LMV43ERDJONRXK43TNFXW4OZXG4YTONJSGI>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[ElJefeDelDesierto]

Thanks dear @vsht !!