Abstract
Implications of the Jacobi identity and Lorentz invariance in the study of equal-time current-field and current-current commutators are discussed. We show that these commutators are related by means of the Jacobi identity. Assuming Lorentz invariance we then prove that equal-time commutators between space components of conserved currents and spinor fields do not have Schwinger terms, provided the same holds for their time components. Moreover, the commutators between the time derivatives of space components of these currents and the field can only have first-order Schwinger terms. These results are also obtained for nonconserved currents whose divergences commute at equal times with the field. In general, equal-time commutators between divergences of currents (or their time derivatives) and fields cannot have first (second) order Schwinger terms. Connections with usual quark and field algebra relations are discussed.
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