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We formulate the hadronic tensor $W_{\mu\nu}$ of deep inelastic scattering inthe path-integral formalism. It is shown that there are 3 gauge invariant andtopologically distinct contributions. Besides the valence contribution, thereare two sources for the sea -- one in the connected insertion and the other inthe disconnected insertion. The operator product expansion is carried out inthis formalism. The operator rescaling and mixing reveal that the connected seapartons evolve the same way as the valence, i.e. their evolution is decoupledfrom the disconnected sea and the gluon distribution functions. We explore thephenomenological consequences of this classification in terms of the small xbehavior, Gottfried sum rule violation, and the flavor dependence. Inparticular, we point out that in the nucleon $\bar{u}$ and $\bar{d}$ partonshave both the connected and disconnected sea contributions; whereas, $\bar{s}$parton has only the disconnected sea contribution. This difference between$\bar{u} + \bar{d}$ and $\bar{s}$, as far as we know, has not been taken intoaccount in the fitting of parton distribution functions to experiments.Comment: Revised version to appear in PR

Parton degrees of freedom from the path-integral formalism