When a mass term does not represent a mass

Abstract

The definition of mass of a scalar field in a curved space has often been generalized by grouping coupling terms between the field and the Ricci curvature with non-curvature-related mass terms. In a broader point of view, one sees that a common misunderstanding resulting from such an identification leads one, in the case of the spin 2 field, to regard the cosmological constant as a non-vanishing mass of cosmological origin for the graviton. Similarly, there are inconsistencies for the spin 1 field. Instead, the intrinsic mass of a field should be regarded as being independent of the background curvature.