Scalar spinor fields interaction in de Sitter ambient space formalism

TL;DR

This paper calculates the interaction matrix elements of scalar and spinor fields in de Sitter space, fixing auxiliary vectors by comparing with Minkowski space results, thus bridging curved and flat spacetime quantum field theories.

Contribution

It provides a method to determine constant five-vectors in de Sitter ambient space formalism by matching interaction matrix elements with Minkowski space in the null curvature limit.

Findings

Calculated tree-level S-matrix elements for scalar-spinor interactions in de Sitter space.

Fixed the auxiliary five-vectors by comparing de Sitter and Minkowski space results.

Established a connection between curved spacetime quantum fields and flat spacetime counterparts.

Abstract

In de Sitter ambient space formalism, the massless minimally coupled scalar field can be constructed from a massless conformally coupled scalar field and a constant five-vector $A^{\alpha}$. Also, a constant five-vector $B^{\alpha}$ appears in the interaction Lagrangian of massless minimally coupled scalar and spinor fields in this formalism. These constant five-vector fields can be fixed in the interaction case in the null curvature limit. Here we will calculate the $\cal S$ matrix elements of scalar-spinor fields interaction in the tree level approximation. Then the constant five-vectors $A^{\alpha}$ and $B^{\alpha}$, will be fixed by comparing the $\cal S$ matrix elements in the null curvature limits with the Minkowskian counterparts.