Massless, string localized quantum fields for any helicity

Abstract

For any massless, irreducible representation of the covering of the proper, orthochronous Poincaré group we construct covariant, free quantum fields that generate the representation space from the vacuum and are localized in semi-infinite strings in the sense of commutation or anti-commutation of the field operators at space-like separation of the strings. Besides the space-like string direction the field operators carry a spinor or tensor index for one of the finite dimensional representations D(j2,k2) of SL(2,C). For given (j, k) the possible integer or half-integer values that the helicity h can take are for string fields only restricted by the condition |h|≤j+k2, in contrast to the case of point localized fields where h=k2−j2 must hold. For infinite helicity no additional index on the string-field is needed in the Bose case while in the Fermi case the fields carry an additional spinor index. For finite helicity we consider in particular string-localized fields that are generalized potentials for point localized fields. The short distance behavior of their two-point functions is independent of the helicity.