  In this paper, we derive the Carrollian amplitude in the framework of bulk
reduction. The Carrollian amplitude is shown to relate to the scattering
amplitude by a Fourier transform in this method. We propose Feynman rules to
calculate the Carrollian amplitude where the Fourier transforms emerge as the
integral representation of the external lines in the Carrollian space. Then we
study the four-point Carrollian amplitude at loop level in massless $\Phi^4$
theory. As a consequence of Poincar\'e invariance, the four-point Carrollian
amplitude can be transformed to the amplitude that only depends on the cross
ratio $z$ of the celestial sphere and a variable $\chi$ invariant under
translation. The four-point Carrollian amplitude is a polynomial of the
two-point Carrollian amplitude whose argument is replaced with $\chi$. The
coefficients of the polynomial have branch cuts in the complex $z$ plane. We
also show that the renormalized Carrollian amplitude obeys the Callan-Symanzik
equation. Moreover, we initiate a generalized $\Phi^4$ theory by designing the
Feynman rules for more general Carrollian amplitude.
