12·î24Æü(ÌÚ) 13:30 -- 15:00 Âçµ×ÊÝ ÆÆ»Ö (µþÅÔÂç³Ø¾ðÊó³Ø¸¦µæ²Ê)
``A mathematical study of the Derezinski-Gerard model''
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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.