Consider the Lagrangian(adsbygoogle = window.adsbygoogle || []).push({});

$$\mathcal{L}=\frac{1}{2}\partial_{\mu}h\partial^{\mu}h-\frac{1}{2}m^{2}h^{2}-\frac{\lambda}{3!}h^{3}$$

for a real scalar field ##h##.

This is the Klein-Gordon Lagrangian with a cubic self-interaction term.

Does this model allow the decay process

$$h \rightarrow h + h?$$

Clearly, in the rest frame, the incoming scalar is at rest, so its total energy is its rest energy, and therefore, it cannot decay to two copies of itself (with twice the rest energy), as that would violate energy conservation?

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# A Possible decay process for a cubic scalar self-interaction

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