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I have learned that chirality is a concept, that appears for $$(A,B)$$ representations of the Lorentz group, where $$A\neq B$$.
An example would be a Dirac spinor, corresponding to the representation $$(\tfrac{1}{2},0)\oplus(0,\tfrac{1}{2})$$, where we can identify left- and right-chiral components.
Wikipedia lists the electromagnetic field strength tensor $$F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$$ as transforming under the $$(1,0)\oplus(0,1)$$ representation of the Lorentz group.