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*The Lagrangian for the graviton is heuristically ##\mathcal{L}=-\frac{1}{2}h\Box h + \frac{1}{3}\lambda h^{3}+Jh,## where ##h## represents the gravitational potential. We are ignoring spin and treating gravity as a simple scalar field theory. The ##h^3## term represents a graviton self-interaction, which is present in general relativity and so ##\lambda \sim \sqrt{G_N}##. The equations of motion are ##\Box h -\lambda h^{2}-J=0##.*

Why the ##h^{3}## term represent the

*graviton self-interaction*? What does

*self-interaction*mean anyway? Does it mean the interaction among the various excitations of the graviton field?