 Dimension-six operators of a real scalar field

In four dimensions, a real scalar field and a partial derivative each have mass dimension one. Seven scalar monomials of dimension six can be listed before integration by parts: ${\varphi }^6$, ${\varphi }^2(\partial \varphi {)}^2$, ${\varphi }^3\square \varphi$, $\varphi {\square }^2\varphi$, ${\partial }_{\mu }\varphi {\partial }^{\mu }\square \varphi$, $(\square \varphi {)}^2$, and $({\partial }_{\mu }{\partial }_{\nu }\varphi {)}^2$. They reduce to the three displayed representatives modulo total derivatives. Leading equations of motion reduce them further to a single new ${\varphi }^6$ interaction, together with shifts of the existing mass and quartic coupling constant.