12·î24Æü(ÌÚ) 13:30 -- 15:00 Âçµ×ÊÝ ÆÆ»Ö (µþÅÔÂç³Ø¾ðÊ󳨏¦µæ²Ê) ``A mathematical study of the Derezinski-Gerard model'' ¡ã¸¦µæÈ¯É½Í׻ݡä We study the Derezinski-Gerard model introduced by Derezinski and Gerard in 1999 as an abstract mathematical one describing interaction between quantum particles and a quantum field. We discuss existence of a ground state of the model and its scaling limit. We give a sufficient condition that the massless Derezinski-Gerard model has a ground state without assumptions about the compactness of the resolvent or the Hamiltonian of quantum particles. We remark that it is a new point in the study of the model. We establish a scaling limit for the model, which is also new. We derive the effective potential of the model by taking its scaling limit.