# Why nf is defined modulus -1 in sitetype "fermion" "electron"

**URL:** <https://itensor.discourse.group/t/why-nf-is-defined-modulus-1-in-sitetype-fermion-electron/2141>\
**Category:** ITensor Julia Questions\
**Created:** [November 27, 2024, 6:49am UTC](https://itensor.discourse.group/t/why-nf-is-defined-modulus-1-in-sitetype-fermion-electron/2141 "2024-11-27T06:49:46Z")\
**Posts on this page:** 1\
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**Author:** ![miles](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/miles/32/6_2.png) [@miles](https://itensor.discourse.group/u/miles)\
**Post date:** [November 27, 2024, 3:12pm UTC](https://itensor.discourse.group/t/why-nf-is-defined-modulus-1-in-sitetype-fermion-electron/2141/2 "2024-11-27T15:12:07Z")

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The idea behind having the last number (the “modulus”) being negative is that the group or symmetry for fermions is not a regular U(1) but a “fermionic” U(1), which some authors have written as fU(1). So the minus sign is to indicate that. In our code currently, it is just a convenient way to distinguish a fermionic Abelian symmetry from a regular one, and we do use this in our experimental “auto fermion” system. You can see it being checked on the following line of code:  
[https://github.com/ITensor/ITensors.jl/blob/795042b976729ed79768482e01f2c4d31b6325ff/src/fermions/fermions.jl#L23](https://github.com/ITensor/ITensors.jl/blob/795042b976729ed79768482e01f2c4d31b6325ff/src/fermions/fermions.jl#L23)

I think what you are doing is the recommended approach for now, which is to define your own QN’s that are supposed to be compatible with the ones from our definitions in the same way.

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