2002/09/24 by Renat Kh. Gainutdinov, R. Kh. Gainutdinov, Gainutdinov, Renat Kh. +2
Physics and Astronomy · #FOS: Physical sciences #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0209129
Invited chapter in "Trends in Field Theory Research", Nova Science Publishers, Inc.: New York. 2004; 36 pages
openalex publication_date 2002/09/24 · arxiv created 2005/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Problems connected with non-Hamiltonian nature of low energy nucleon dynamics in the effective field theory (EFT) of nuclear forces is investigated by using the formalism of the generalized quantum dynamics (GQD) developed in [J. Phys. A, 5657 (1999)]. This formalism is based on a generalized dynamical equation derived as the most general equation of motion consistent with the current concepts of quantum physics. By using the example of the EFT of nuclear forces, we demonstrate that a theory, which, being formulated in terms of Hamiltonian formalism, leads to ultraviolet divergences, may manifest itself as a perfectly consistent theory free from infinities, if it is considered from the more general point of view provided by the GQD. We show that non-Hamiltonian character of nucleon dynamics gives rise to some new problems connected with discontinuity of the evolution operator. This discontinuity results in the fact that the Hilbert space of nucleon states cannot be realized in the standard way. A space which allows one to realize, in a natural way, the Hilbert space of nucleon states is investigated. The structure of this space reflects the existence of the high energy degrees of freedom which affect on low energy nucleon dynamics.