Causality and Renormalization in Finite-Time-Path Out-of-Equilibrium $\phi^3$ QFT

Ivan Dadić
Institute Ruđer Bošković, Zagreb

This talk is based on work with Prof. Dr. D. Klabucar.

We formulate the perturbative renormalization for the out-of-equilibrium $g \phi^3$ quantum field theory in the formalism with the finite time path. We use the retarded/advanced basis of out-of-equilibrium Green functions. We use the dimensional regularization method and find the correspondence of diverging contributions in the Feynman diagrams and their counterparts in R/A basis.

1. The tadpole contributions are only partially eliminated by renormalization condition. But, finite tadpole contributions are vanishing as $t\rightarrow \infty $, in a good agreement with the renormalization condition $<0|\phi|0>=0$ of the S-Matrix theory.
2. Renormalized finite part of retarded (advanced) self-energy $\Sigma_{\infty,R(A)}(p_0)$ is not retarded (i.e. not causal), as it is not vanishing when $|p_0|\rightarrow\infty $. The same happens in S-matrix theory, where $\Sigma_{\infty,F}(p_0)$ cannot be split into it's retarded and advanced component. The problem is ``avoided '' by considering self-energy with legs $G_F(p_0)\Sigma_{\infty,F}(p_0)G_F(p_0)$, which can be split to R and A components. The same works in the Glaser-Epstein renormalisation approach. In the finite-time-path approach $G_R*\Sigma_R*G_R$ should be calculated at $D\neq 4$.
3. We find the causality problem to be more severe in S-matrix theory, where the accausal information is possible (i.e. information from future).