BCFW Recursion Relation with Nonzero Boundary Contribution

TL;DR

This paper extends the BCFW recursion relation to cases with nonzero boundary contributions, enabling its application to a broader class of theories like lambda-phi-four and Yukawa couplings.

Contribution

It introduces a method to incorporate boundary contributions into BCFW recursion relations for theories where boundary terms cannot be eliminated.

Findings

Successfully derived BCFW recursion with boundary contributions for specific theories.

Demonstrated the approach on lambda-phi-four theory and fermion-scalar Yukawa coupling.

Showed that boundary effects can be analyzed and included in recursion relations.

Abstract

The appearance of BCFW on-shell recursion relation has deepen our understanding of quantum field theory, especially the one with gauge boson and graviton. To be able to write the BCFW recursion relation, the knowledge of boundary contributions is needed. So far, most applications have been constrained to the cases where the boundary contribution is zero. In this paper, we show that for some theories, although there is no proper deformation to annihilate the boundary contribution, its effects can be analyzed in simple way, thus we do able to write down the BCFW recursion relation with boundary contributions. The examples we will present in this paper include the lambda-phi-four theory and Yukawa coupling between fermions and scalars.