On the Connection of Spin and Commutation Relations between Different Fields

Abstract

The connection of spin and commutation relations for different fields is studied. The normal locality is defined as the property that two Boson fields as well as a Boson field and a Fermion field commute, while two Fermion fields anticommute with each other at a spacelike distance. A regular locality is defined as any combination of commutativity and anticommutativity between various pairs of fields at spacelike distance, where the kinematically related fields are assumed to obey the same type of commutation relations. The normal and regular weak locality is defined in a corresponding way. It is proved on the basis of the Lorentz invariance and spectrum conditions that any regular locality is equivalent to the normal locality plus a set of even‐oddness conservation laws. It is further shown, under the assumption of the normal weak locality between pairs of the same field, that any regular weak locality is equivalent to the normal weak locality plus a set of even‐oddness conservation laws.