Amplitudes within causal loop-tree duality

Abstract

We study scalar one-loop amplitudes in massive ${\ensuremath{\phi}}^{3}$-theory within causal loop-tree duality. We derive a recurrence relation for the integrand of the amplitude. The integrand is by construction free of spurious singularities on H-surfaces. Taking renormalization and contour deformation into account, we obtain the (integrated) amplitude by Monte Carlo integration. We have checked up to seven points that our results agree with analytic results.