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- Is a term proportional to ##\phi## valid in a scalar Lagrangian?

Hi, if I want to construct the most general Lagrangian of a single scalar field up to two fields and two derivatives, I usually see that is

$$\mathscr{L} = \phi \square \phi + c_2 \phi^2$$ i.e. the Klein-Gordon Lagrangian.

My question is, would be valid the Lagrangian

$$\mathscr{L} = \phi \square \phi + c_1 \phi + c_2 \phi^2$$

?

$$\mathscr{L} = \phi \square \phi + c_2 \phi^2$$ i.e. the Klein-Gordon Lagrangian.

My question is, would be valid the Lagrangian

$$\mathscr{L} = \phi \square \phi + c_1 \phi + c_2 \phi^2$$

?