Unparticle in (1+1) dimension with one loop correction

Abstract

The possibility of the presence of unparticle has been discussed recently adding a mass like term for gauge field with the Vector Schwinger model at the classical level \cite{GEOR1}. A one loop correction due to bosonization is taken into account and investigation is carried over to study the effect of it in connection with the unparticle scenario. It has been found that mass of the gauge boson acquires a generalized expression with the bare coupling constant and the parameters involved in the masslike terms added at the classical level term as well the terms entered in the model during the one loop correction needed for bosonization. So the physical mass viz., unparticle scale gets a new definition. The fermionic propagator is calculated which also agrees with the generalized mass term. A novel restoration of the lost gauge invariance reappears when the ambiguity parameter that entered into the effective action within the one loop correction acquires a specific expression with the bare coupling constant and the parameter involved in the masslike term of the gauge field added at the classical level.