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.

Bertini, M., Noja, D., Posilicano, A. (2018). A note on the infrared problem in model field theories. RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI, 39(2), 217-228.

A note on the infrared problem in model field theories

Diego Noja;
2018

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.
Articolo in rivista - Articolo scientifico
Infrared divergence; Quantum fields;
Quantum field theories, Infrared problem, Van Hove model
English
2018
39
2
217
228
none
Bertini, M., Noja, D., Posilicano, A. (2018). A note on the infrared problem in model field theories. RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI, 39(2), 217-228.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/214480
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