Fermi Motion in Nucleons and the Generalized Heisenberg Uncertainty Relation

Abstract

In a series of our papers (e.g., A.L. Kholmetskii, et al. Ann. Phys. 392, 49 (2018)) we proposed to redefine the momentum operator for an electrically charged quantum particle in an electromagnetic (EM) field through the sum of its mechanical momentum ( P M ) and the interactional electromagnetic momentum ( P EM ), instead of the standard definition of this operator, associated with the canonical momentum of the particle. In the present contribution, we represent our three-step way to the new momentum operator and focus on one of its principal implications, named the "generalized Heisenberg uncertainty relation", where, in comparison to its standard form, the mechanical momentum of a charged particle P M is replaced by the sum of P M and P EM . We then apply the generalized uncertainty relation to the analysis of the Fermi motion of quarks in the proton and neutron and show that a quark with a unique charge (i.e., the d-antiquark in the proton and the u-antiquark in the neutron) should have a more narrow momentum distribution compared to the wider momentum distribution of the remaining quarks (the two u-quarks in the proton and the two d-quarks in the neutron) in their Fermi motion. The agreement of these results with the available experimental data does not touch the validity of the results of calculation of quantum chromodynamics (QCD) regarding the description of the proton and neutron, but rather enriches their physical interpretation.