Volume 39_2_(2018)_217-228

A note on the infrared problem in model field theories.
Massimo Bertini, Diego Noja, Andrea Posilicano

Abstract. In this note we critically re-examine the usual procedure of quantization of classical wave equations with static sources. We point out that the origin of infrared difficulties in the so called van Hove model is related to the complex Hilbert space structure one puts on the classical phase space and the corresponding unitarization of the classical symplectic evolution. Whereas in the usual framework the condition of infrared regularity forces the total charge of the external source to vanish, in our setting the infrared regularity condition is equivalent to having a source with a finite (electrostatic) energy. A similar analysis could be applied to models of field-particle interaction such as the Nelson model.

Rend. Mat. Appl. (7) 39 (2018) 217-228;  pdf