Commutation Relations of Baryon "Currents"

The notion of baryon "currents" is introduced. We make the hypothesis [partially conserved baryon currents (PCBC)] that the divergences of these baryon currents are related to baryon fields in much the same way that the hypothesis of partially conserved axial-vector current (PCAC) relates the divergences of axial-vector meson currents to pseudoscalar meson fields. On the basis of the quark model, we construct the baryon currents as linear combinations of the products of three quarks. Using the canonical anticommutation relations for the quarks, we derive the equal-time commutation relations of the baryon currents with vector and axial-vector meson currents. The right-hand sides of these commutation relations turn out to be linear combinations of the baryon currents themselves. As applications we consider the matrix elements of the commutation relations (1) between vacuum and baryon states and (2) between meson and baryon states. The results consist of algebraic relations between various form factors, which can be checked, in principle, by accurate experimental data when available.