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We are developing a new problem-solving methodology based on a self-organization paradigm. To realize our future goal of self-organizing computational systems, we have to study computation based on local information and its emergent behavior, which are considered essential in self-organizing systems. This paper presents a stochastic (or nondeterministic)… (More)
We study the infrared catastrophe for Nelson’s Hamiltonian, which has the external potential in a general class. We show that both, the divergence of the total number of soft photons and non-existence of any ground state, are due to the common reason under general conditions.
We consider a massless scalar Bose field interacting with two particles, one of them infinitely heavy. Neither an infrared nor an ultraviolet cutoff is imposed. In case the charge of the particles is of the same sign and sufficiently small, we prove the existence of a ground state.
In the Nelson model particles interact through a scalar massless field. For hydrogen-like atoms there is a nucleus of infinite mass and charge Ze, Z > 0, fixed at the origin and an electron of mass m and charge e. This system forms a bound state with binding energy Ebin = me Z/2 to leading order in e. We investigate the radiative corrections to the binding… (More)
We derive a mathematical mechanism of infrared catastrophe from the idea for the proof in [22, 23] and generalize it so that we can apply it to several models in quantum field theory. We define the Carleman operator from the operator-theoretical pull-through formula on ground states. Characterizing infrared catastrophe by the Carleman operator, we study the… (More)
Regularities and higher order regularities of ground states of quantum field models are investigated through the fact that asymptotic annihilation operators vanish ground states. Moreover a sufficient condition for the absence of a ground state is given.
Author(s) Arai, Asao; Hirokawa, Masao Citation Reviews in Mathematical Physics, 13(4): 513-528 Issue Date 2001-04 Doc URL http://hdl.handle.net/2115/38266 Right Electronic version of an article published as Reviews in Mathematical Physics, Vol. 13, Issue 4, 2001, pp. 513-528, DOI: 10.1142/S0129055X01000740 © World Scientific Publishing Company,… (More)
We give a functional integral representation of the semigroup generated by the spin-boson Hamiltonian by making use of a Poisson point process and a Euclidean field. We present a method of constructing Gibbs path measures indexed by the full real line which can be applied also to more general stochastic processes with jump discontinuities. Using these tools… (More)
Dear IAMP Members, according to Part I of the By-Laws we announce a meeting of the IAMP General Assembly. It will convene on Monday August 3 in the Meridian Hall of the Clarion Congress Hotel in Prague opening at 8pm. The agenda: 1) President report 2) Treasurer report 3) The ICMP 2012 a) Presentation of the bids b) Discussion and informal vote 4) General… (More)