The infrared behaviour in Nelson's model of a quantum particle coupled to a massless scalar field
Lorinczi, Jozsef ; Minlos, Robert A. ; Spohn, Herbert
arXiv, 0011043 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-11-27
Classification:  Mathematical Physics,  Mathematics - Geometric Topology,  Mathematics - Probability 
@article{0011043,
     author = {Lorinczi, Jozsef and Minlos, Robert A. and Spohn, Herbert},
     title = {The infrared behaviour in Nelson's model of a quantum particle coupled
  to a massless scalar field},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0011043}
}

Lorinczi, Jozsef; Minlos, Robert A.; Spohn, Herbert. The infrared behaviour in Nelson's model of a quantum particle coupled
  to a massless scalar field. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0011043/