Interacting massive/massless continuous-spin fields and integer-spin fields

In the framework of light-cone gauge approach, interacting continuous-spin fields and integer-spin fields propagating in flat space are studied. The continuous-spin fields are considered by using a light-cone gauge vector superspace formulation. Description of massive continuous-spin fields associated with the principal, complementary and discrete series is presented. For the massive continuous-spin fields of the principal and complementary series and massless continuous-spin fields, all parity-even cubic vertices realized as functions on the light-cone gauge vector superspace are obtained. Cubic vertices for a cross-interaction of massive/massless continuous spin fields and massive/massless integer-spin fields are also derived. The use of the light-cone gauge vector superspace formulation considerably simplifies the cubic vertices as compared to the ones of oscillator formulation. Some cubic vertices realized as distributions are also found. Map between the oscillator formulation and the vector superspace formulation of the continuous-spin fields is explicitly described. An equivalence of the light-cone gauge and Lorentz covariant formulations of the continuous-spin fields is also demonstrated.