Local Field Theory and Isospin Invariance. I. Free-Field Theory of Spinless Bosons

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Abstract
The properties of free-field theories of spinless bosons are investigated. The self-conjugate boson field theories of isospin ½, 32, 52, ⋯ are shown to be nonlocal: the energy, isospin, and number densities fail to commute for spacelike separations. The difficulty is traced to the necessary occurrence of non-independent field variables. For the anomalous case the dependent variables are nonlocally related to the independent ones; elimination of the former makes superficially local quantities depend nonlocally on the independent fields. The connection with canonical field theory is investigated. The p and q coordinates have anomalous commutation relations in the nonlocal case. Although the Hamiltonian appears normal in every case, the anomalous theories are characterized by zero (integrated) Lagrangian. Antiparticle conjugation is investigated in detail with attention to phase questions. For anomalous theories two types of conjugation are found, one of which nonlocally relates the field to a superposition of its adjoint. A unitary transformation is constructed which converts one type to the other. Finally, CPT transformation properties of normal and abnormal theories are derived and compared.