TY - JOUR
T1 - Ultraviolet renormalization of the Nelson Hamiltonian through functional integration
AU - Gubinelli, Massimiliano
AU - Hiroshima, Fumio
AU - Lorinczi, József
N1 - Funding Information:
FH acknowledges support of Grant-in-Aid for Science Research (B) 20340032 from JSPS , and thanks the hospitality of Université d'Aix–Marseille–Luminy, and Université de Rennes 1, and Jozsef Lőrinczi for an invitation on the workshop Lieb–Thirring-Type Bounds for Perturbations of Feller Processes held at Institut Mittag-Leffler in July 2013, where part of this work has been done. JL thanks IHES, Bures-sur-Yvette, for a visiting fellowship, where part of this work has been done, and gratefully thanks Fumio Hiroshima for an invitation to the workshop Quantum Field Theory and Related Topics, held at RIMS Kyoto in November 2012.
Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2014/11/1
Y1 - 2014/11/1
N2 - Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the ultraviolet cutoff limit a self-adjoint operator exists after a logarithmically divergent term is subtracted from the original Hamiltonian. We obtain this term as the diagonal part of a pair interaction appearing in the density of a Gibbs measure derived from the Feynman-Kac representation of the Hamiltonian. Also, we show existence of a weak coupling limit of the renormalized Hamiltonian and derive an effective Yukawa interaction potential between the particles.
AB - Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the ultraviolet cutoff limit a self-adjoint operator exists after a logarithmically divergent term is subtracted from the original Hamiltonian. We obtain this term as the diagonal part of a pair interaction appearing in the density of a Gibbs measure derived from the Feynman-Kac representation of the Hamiltonian. Also, we show existence of a weak coupling limit of the renormalized Hamiltonian and derive an effective Yukawa interaction potential between the particles.
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U2 - 10.1016/j.jfa.2014.08.002
DO - 10.1016/j.jfa.2014.08.002
M3 - Article
AN - SCOPUS:85027955733
SN - 0022-1236
VL - 267
SP - 3125
EP - 3153
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 9
ER -