Nonlocal on-shell field redefinition for the standard-model extension

This work instigates a study of nonlocal field mappings within the Lorentz- and $CPT$-violating standard-model extension (SME). An example of such a mapping is constructed explicitly, and the conditions for the existence of its inverse are investigated. It is demonstrated that the associated field redefinition can remove $b^{\mu }$-type Lorentz violation from free SME fermions in certain situations. These results are employed to obtain explicit expressions for the corresponding Lorentz-breaking momentum-space eigenspinors and their orthogonality relations.