When a mass term does not represent a mass

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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.
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