Are there any methods known for computing the elastic phase shifts in a relativistic QFT such as $(\lambda/4!)\phi^4$, which ensure that unitarity is satisfied?. The naive approach of simply projecting the perturbative scattering amplitude $M(s,t)$ (evaluated below threshold) to the angular momentum eigenbasis does not seem viable, since there’s nothing to ensure that the unitarity constraint $|S_l| = 1$ is satisfied.

For reference, I’m defining $S_l$ as in Eq. (10) of Ref. [1] and the phase shift $\delta_l$ is defined via $S_l = e^{\mathrm{i} 2\delta_l}$. If one plugs, for example, the leading order amplitude $M(s,t)=-\lambda$ for $(\lambda/4!)\phi^4$ into Eq. (10), then it is easy to see that $|S_0| \neq 1$.

[1] https://arxiv.org/abs/1708.06765



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.