arXiv subjects
Publications and source records attributed to Xiang-Song Chen.
We show that in the functional integral formalism of U(1) gauge field theory some formal manipulation such as interchange of order of integration can yield erroneous results. The example studied is analysed by Fubini theorem.
We prove that a kind of averaging procedure for constructing gauge-invariant operators(or functionals) out of gauge-variant ones is erroneous and inapplicable for a large class of operators(or functionals).
We find that sometimes the usual definition of functional integration over the gauge group through limiting process may have internal difficulties.
Based on a canonically derived path integral formalism, we demonstrate that the perturbative calculation of the matrix element for gauge dependent operators has crucial difference from that for gauge invariant ones. For a gauge dependent operator ${\cal O}(ϕ)$ what appears in the Feynman diagrams is not ${\cal O} (ϕ)$ itself, but the gauge-transformed one ${\cal O}(^ωϕ)$, where $ω$ characterizes the specific gauge transformation which brings any field variable into the particular gauge which we have adopted to quantize the gauge theory using the canonical method. The study of the matrix element of gauge dependent operators also reveals that the formal path integral formalism for gauge theory is not always reliable.
We prove that the {\em gauge dependent} gluon spin, gluon and quark orbital angular momenta operators have {\em gauge invariant} expectation values on hadron states with {\em definite} momentum and polarization, therefore the conventional decomposition of nucleon spin into contributions from the spin and orbital angular momentum of quark and gluon is {\em gauge independent}. Similar conclusions apply to the {\em gauge dependent} quark momentum and kinetic energy operators, and accordingly nucleon momentum and mass structures.
A model independent, field theoretical relation between baryon magnetic moment and its spin structure is derived and it is explained why constituent quark model is a good approximation in describing baryon magnetic moments.
A qualitative QCD analysis and a quantitative model calculation are given to show that the constituent quark model remains a good approximation even with the nucleon spin structure revealed in polarized deep inelastic scattering taking into account.
A dynamical valence and sea quark mixing model is shown to fit the baryon ground state properties as well as the spin content of the nucleon. The relativistic correction and the $q^3{\leftrightarrow} q^3q\bar{q}$ transition terms induced by the quark axial vector current $\barψ\vecγγ^5ψ$ in this model space is responsible for the quark spin reduction.