@article{46ef970eee4b4878a32fb474111bb5be,
title = "Ground state for point particles interacting through a massless scalar Bose field",
abstract = "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.",
keywords = "Energy scale renormalization, Gross' canonical transformation, Nelson's Model, Removal of infrared cutoff, Removal of ultraviolet cutoff",
author = "Masao Hirokawa and Fumio Hiroshima and Herbert Spohn",
note = "Funding Information: M. Hirokawa and F. Hiroshima thank for the hospitality at Technische Universit{\"a}t M{\"u}nchen. M. Hirokawa is indebted to his colleagues of the seminar on constructive field theory and renormalization group organized by H. Ezawa at Gakushuin University. He also thanks Griesemer for explaining him that Lemma 5.1 implies Lemma 5.2(ii), and as a consequence Proposition 5.3(ii), (iii), and exponential decay in Proposition 5.4. His work in Japan is supported by JSPS, Grant-in-Aid for Scientific Research (C) 13640215, and his work in Germany by DAAD. F. Hiroshima{\textquoteright}s work is supported by the Graduiertenkolleg {\textquoteleft}{\textquoteleft}Mathematik in ihrer Wechselbeziehung zur Physik{\textquoteright}{\textquoteright} of the LMU Munich and by JSPS, Grant-in-Aid 13740106 for Encouragement of Young Scientists.",
year = "2005",
month = mar,
day = "1",
doi = "10.1016/j.aim.2004.03.011",
language = "English",
volume = "191",
pages = "339--392",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
number = "2",
}