Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case
J. Yu. Panteleeva, Maxim V. Polyakov
Abstract
We derive simple relations which express 2D light front force distributions in terms of 3D Breit frame pressure and shear force distributions. Mathematically the relations correspond to invertible Abel transformation and they establish one-to-one mathematical equivalence of 3D Breit frame force distributions and 2D light front ones. The beauty and simplicity of the Abel transformations allow us to derive a number of new relations for light front force distributions. Any knowledge (model calculation, experimental measurement, etc.) about pressure and shear force distributions in Breit frame can be unambiguously transformed into light front force distributions with the help of Abel transformation. Due to the positivity property of the Abel transformation we obtain an important result---the 2D local stability conditions are satisfied automatically if the corresponding 3D stability conditions are fulfilled. In this way we established not only mathematical equivalence of 2D and 3D forces distributions but also their physics equivalence in terms of stability. As an illustration of how the relations work, we calculated the light front force distributions for a large nucleus as a liquid drop, and for large ${N}_{c}$ nucleon as a chiral soliton.