Conformal Transformations with Multiple Scalar Fields

TL;DR

This paper investigates conditions under which multiple scalar fields with non-minimal couplings can be transformed into a canonical form, revealing that such transformations are generally limited to models with two fields.

Contribution

It identifies specific conditions allowing conformal transformations to canonical form in multi-scalar field models, highlighting limitations beyond two fields.

Findings

Two-field models can be transformed to canonical form under certain conditions.

Models with more than two non-minimally coupled fields generally cannot be transformed.

The study clarifies the scope of conformal transformations in multi-scalar theories.

Abstract

Many interesting models incorporate scalar fields with non-minimal couplings to the spacetime Ricci curvature scalar. As is well known, if only one scalar field is non-minimally coupled, then one may perform a conformal transformation to a new frame in which both the gravitational portion of the Lagrangian and the kinetic term for the (rescaled) scalar field assume canonical form. We examine under what conditions the gravitational and kinetic terms in the Lagrangian may be brought into canonical form when more than one scalar field has non-minimal coupling. A particular class of two-field models admits such a transformation, but models with more than two non-minimally coupled fields in general do not.