Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The infrared behaviour in Nelson's model of a quantum particle coupled
  to a massless scalar field   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.

31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat