Abstract: We derive a mathematical mechanism of infrared catastrophe in a general framework. We define the Carleman operator from the operator-theoretical pull-through formula on ground states. Characterizing infrared catastrophe by this operator, we study the mechanism of infrared catastrophe through the domain of the Carleman operator. As applications of our results, we consider the generalized spin-boson model and generalized Lee-Pines model. For the latter model we prove that the infrared singularity condition causes not only the infrared catastrophe but also the infinite uncertainty of the position of the nonrelativistic particle dressing itself in the cloud of soft bosons indirectly.