Amplitudes within causal loop-tree duality

Abstract

We study scalar one-loop amplitudes in massive ${\varphi }^3$-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 renormalisation 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.

Comments: 43 pages, v2: version to be published, v3: some typos fixed