Critical scaling for spectral functions

We study real-time scalar φ ⁴ ϕ 4 -theory in 2+1 dimensions near criticality. Specifically, we compute the single-particle spectral function and that of the s -channel four-point function in and outside the scaling regime. The computation is done with the spectral functional Callan–Symanzik equation, which exhibits manifest Lorentz invariance and preserves causality. We extract the scaling exponent η η from the spectral function and compare our result with that from a Euclidean fixed point analysis.