Currents in the Non-Linear Realization of a Group on Its Sub-Group
Takao Okabayashi · Progress of Theoretical Physics · 1971
In the non-linear realization of a group on its sub-group, there is a method to define currents which can be classified between the Lagrangian formalism and the local current algebra in respect of the model dependence. In addition to the minimum condition that a current should be a base vector of a linear adjoint representation, some additional requirements which depend on models very loosely are imposed. Then the current can be defined uniquely without any reference to the equations of motion of the constituent fields, and the types of the symmetry violation and the models are restricted. The violation should be additive in the language of Lagrangian formalism, and the field-current identity hypothesis, for example, is not applicable to the non-linear realization. Furthermore there is no quantization method which is consistent with the local current algebra.