Does field redefinition make Klein Gordon Action unhealthy?

Question

Consider the action $L=\chi\square^3\chi$

On one hand, Ostrogradski's theorem seems to indicate that it is not unitary.

On the other hand, it can be reached by replacing $\phi$ with $\square \chi$ in KleinGordon action.

Namely, KleinGordon Action is well known to be healthy. Now if we replace in it with $\phi=\square\chi$, we get the action $L=\chi\square^3\chi$.

 

Does this make the Klein Gordon Action unhealthy?

Comments

Hi Xavier, what exactly do you mean by healthy? Do you mean useful as an effective action? As I understand it, non-unitarity is always a bad thing ...

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Sorry, my bad choice of title, I've reedited the question, please review it, I'll be waiting for comments

Answer 1

The apparent answer seems to be yes, and it means we'd better not do this kind of redefinition?

Comments

then I would be interested in what restrictions do we follow when doing field redefinitions. I ask this because when we analyze higher spin fields with stuckelberg trick, we need to do field redefinitions which contains derivatives.