Breaking of scale invariance and behavior of the spectral function in the Jost–Lehmann–Dyson representation

A calculation is made of the behavior of the spectral function $\psi(|\mathbf u|, \lambda^2)$ of the Jost–Lehmann–Dysen representation as $\lambda^2\to\infty$ and $|\mathbf u|\to0$ in the ladder $\varphi^3$ and $\varphi^4$ models. It is shown that in the case of the q 4 model, for which scale invarianee is broken, the spectral function does not factorize with respect to the variables as $\lambda^2\to\infty$ and that its growth with respect to $\lambda^2$ depends essentially on $|\mathbf u|$.