Application of density matrix to the description of the scaling properties of deep inelastic electron scattering

The electroproduction of hadrons in the deep inelastic region is described by means of a density matrix in the framework of the one-time formalism in quantum field theory. It is shown that in the approximation of single-photon interaction of the electron and proton, considered as a whole, the inclusive cross section satisfies ordinary Björken scaling. In the general case of many-photon exchange, the cross section also satisfies the scaling law and depends on two variables, the Björken and Eeynman variables. In the case when the interaction of the electron with the individual constituent particles of the protons is assumed to be a single-photon interaction (the interaction of the electron with the proton as a whole remaining a many-photon interaction), the inclusive cross section depends on a single variable which differs from the Björken variable and may be expressed as a combination of the Björken and Feynman variables.