The equations of motion of any special relativistic (quantum or classical) field theory must be Lorentz covariant. For this reason, when writing down a Lagrangian (density) it is generally assumed that the Lagrangian must be a Lorentz scalar, since this always generates a Lorentz covariant equation. However, it is possible (c.f. this stack exchange post) for an equation of motion to possess symmetries that its action does not. Is is possible for a Lagrangian that is not a Lorentz scalar to generate a Lorentz covariant equation of motion? If so, are there any prominent examples?
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Possible duplicate: https://physics.stackexchange.com/q/237302/2451 – Qmechanic May 03 '21 at 16:53
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That question is in a similar spirit, but my question is definitely different. – xzd209 May 04 '21 at 10:02