Using dimensional regularization we renormalize the Lee model in arbitrary space-time dimension $D$. We compute $\beta \mathrm{}\left(g\right)\mathrm{}$ and $\gamma \mathrm{}\left(g\right)\mathrm{}$, the coefficient functions of the Callan-Symanzik equation, in closed form and show that the model is asymptotically free when $D<\mathrm{}4\mathrm{}$. In addition, we demonstrate a strict correlation between the sign of $\beta \mathrm{}\left(g\right)\mathrm{}$ and the presence of a ghost state: There is no ghost when $\beta \mathrm{}\left(g\right)<0\mathrm{}$. Finally, we study an extended Lee model with two coupling constants and study the behavior of the effective coupling constants in the deep-Euclidean region.

• Received 7 May 1974

DOI:https://doi.org/10.1103/PhysRevD.10.1753