Hello everyone, I'm trying to write down a Lagrangian invariant under local ISO(3) (rotations+shifts) transformations. I'm working at classical level and there will be no quantization of any kind so the theory shouldn't have any ghost pathology.(adsbygoogle = window.adsbygoogle || []).push({});

However, I found that, out of the 6 gauge fields needed, 3 of them are non-dynamical, i.e. they don't admit a kinetic term in the Lagrangian but they only appear in the covariant derivative of the fields, like a source. However, they also transform non-trivially under local ISO(3) (of course).

Is there anything pathologically wrong in it or can I just accept the fact that they are non-dynamical?

Thanks a lot!

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# Gauge theory with non-dynamical gauge field

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