Renormalization of theδexpansion of λ(φ2+2δ)2theory

We study a new artificial expansion method, the δ expansion, which interpolates between a soluble interaction λ${\phi }^2$ and the interaction of interest λ${\phi }^4$ using the form λ(${\phi }^{2+2\delta }$). The δ expansion is applied to a scalar field theory with an interaction λ(${\phi }^{2+2\delta }$) in two dimensions. The two-point, four-point, and six-point one-particle-irreducible Green’s functions are calculated through third order in δ. The theory is renormalized and it is found that in a class of prescriptions the δ expansion of λ(${\phi }^{2+2\delta }$ ${)}_2$ reproduces the standard weak-coupling expansion of λ(${\phi }^4$ ${)}_2$ for all δ>0. All other renormalization prescriptions make the theory equivalent to λ(${\phi }^{2P}$ ${)}_2$ for an arbitrary positive integer P.