@article{2184c0ef3f4c495c9477d57ca720d0ff,
title = "The infrared behaviour in Nelson's model of a quantum particle coupled to a massless scalar field",
abstract = "We prove that Nelson s massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian has no ground state in Fock space and thus it is not unitarily equivalent with the Hamiltonian obtained from Euclidean quantization. In contrast, for dimensions higher than three the Nelson Hamiltonian has a unique ground state in Fock space and the two Hamiltonians are unitarily equivalent. We also show that the Euclidean Hamiltonian has no spectral gap.",
author = "J. L{\"o}rinczi and Minlos, {R. A.} and H. Spohn",
note = "Funding Information: Thus Lˆ1(y)2Lˆ2(y) ∼ |y|2d+γ−5. The asymptotics of the integral at the right hand side of (6.9) becomes then 1/t2d+γ−4. Note that for d ≥ 3 and γ > 0, 2d + γ − 4 > d − 1, and thus the second term in (6.5) is o(1/td−1). This completes the proof. □ Acknowledgments. J.L. is supported by Deutsche Forschungsgemeinschaft within Schwerpunktprogramm “Interagierende stochastische Sy steme von hoher Kom-plexit{\"a}t”. R.A.M. thanks Zentrum Mathematik of Technische Universit{\"a}t M{\"u}nchen for warm hospitality and financial support. He also thanks the Russian Fundamental Research Foundation (grants 99-01-00284 and 00-01-00271) and CRDF (grant NRM 1-2085) for financial support.",
year = "2002",
doi = "10.1007/s00023-002-8617-6",
language = "English",
volume = "3",
pages = "269--295",
journal = "Annales Henri Poincare",
issn = "1424-0637",
publisher = "Birkhauser Verlag Basel",
number = "2",
}