The infrared behaviour in Nelson's model of a quantum particle coupled to a massless scalar field

2000/11/27 by Jozsef Lorinczi, Robert A. Minlos, Herbert Spohn
Physics and Astronomy · Mathematics · #math-ph #math.GT #math.MP #math.PR

paper · pdf

published as Annales Henri Poincare 3 (2002) 269-295

arxiv created 2000/11/27 · arxiv updated 2009/11/30

Abstract

We prove that Nelson's massless scalar field model is infrared divergent in three dimensions. In particular, the Nelson Hamiltonian and the Hamiltonian obtained from Euclidean quantization are not unitarily equivalent. 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.

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