- 00-467 Jozsef Lorinczi, Robert A. Minlos, Herbert Spohn
- The infrared behaviour in Nelson's model of a quantum
particle coupled to a massless scalar field
Nov 24, 00
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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.