Decay of a scalar condensate in two different approaches

A bstract Decay of a scalar condensate via interactions with (quasi-)particles is of interest to many fields in physics, including cosmology. In cosmology, the decay of an inflaton condensate leads to the production of daughter particles and reheating of the Universe. In computing the decay rate, two quantum field theoretic approaches can be found in the literature: one is based on parametric resonance of mode functions of the daughter particle; another is based on the S -matrix of a coherent state and Feynman-diagrammatic perturbation theory. We modify the latter from the previous literature in a way that manifests what we are computing and does not include unwanted Feynman diagrams. We notice the equivalence of these two approaches and demonstrate it by explicitly computing the decay rate at lower orders in the double expansion of the amplitude of coherent oscillation (or narrow resonance) and velocity of the daughter particle.