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## Homework Statement

Show that $$L=\phi\Box^2\phi$$ generates negative energy density.

## Homework Equations

## The Attempt at a Solution

The energy density is $$E=\frac{\partial L}{\partial \dot{\phi}}\dot{\phi}-L$$ Also the Lagrangian can be rewritten (using divergence theorem) as $$L=-\partial_\mu\phi\partial_\mu(\Box\phi)$$ So I would get $$E=-\partial_0\phi\partial_0(\Box\phi)+\partial_\mu\phi\partial_\mu(\Box\phi)$$ $$E=-\partial_x\phi\partial_x(\Box\phi)-\partial_y\phi\partial_y(\Box\phi)-\partial_z\phi\partial_z(\Box\phi)$$. Why is this negative necessarily? Thank you!