The two ways of gauging the Poincare' group

TL;DR

This paper explores two methods of describing gravity as a gauge theory of the Poincare' group, emphasizing the role of pseudo-translations in maintaining consistency with the Equivalence Principle.

Contribution

It introduces the concept of pseudo-translations and provides explicit formulas, enhancing the geometric understanding of gauge theories of gravity.

Findings

Gauge theories of gravity require pseudo-translations for consistency.

Explicit expressions for pseudo-translations are derived.

Pseudo-translations may aid in supergravity geometric interpretations.

Abstract

A description of how a theory of gravity can be considered as a gauge theory (in the sense of Trautman) of the Poincare' group is given. As a result, it is shown that a gauge theory of this kind is consistent with the Equivalence Principle only if the Lagrangian and the constraints are preserved not only by the gauge transformations but also by an additional family of transformations, called "pseudo-translations". Explicit expressions of pseudo-translations and of their action on gravitational gauge fields are given. They are expected to be useful for geometric interpretations of their analogues in supergravity theories.