Forward scattering amplitudes in the imaginary time formalism

@article{Brandt2021ForwardSA,
  title={Forward scattering amplitudes in the imaginary time formalism},
  author={Fernando T. Brandt and J. Frenkel and S. Martins-Filho and D. G. C. McKeon and G. S. S. Sakoda},
  journal={Physical Review D},
  year={2021}
}
We study, in the imaginary time formalism, the relation between loops and on-shell forward scattering tree amplitudes in thermal field theories. This allows for an efficient evaluation, at all temperatures, of Green’s functions with causal retarded boundary conditions. We present an application of this relation in quantum gravity coupled to scalar matter fields. We show that at one or two loops, involving planar diagrams, the 1PI retarded thermal Green’s functions may respectively be expressed… 

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