It's a famous claim that spin-0, spin-1 and spin-2 fields are described by scalar, vector and second-rank tensor, respectively. My question is: why not other objects? For example, consider spin-1 field, we can use a field that carries two left spinor indexes. From the group-theoretic relation we know it contains a scalar component and a spin-1 component, the same as the vector representation.(adsbygoogle = window.adsbygoogle || []).push({});

This claim is first recognized (to my knowledge) on a classic paper (Fierz 1939 Helv. Phys. Acta, 12, 3), but it's in German and I can't find the English version online. Can anyone help me understand it? Thanks.

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# Why is spin-1 field described by a vector field?

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