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Abstract A transformation is introduced in momentum representation to keep a covariant description at every stage of a loop computation in gravity. The procedure treats on equal footing local internal and space-time symmetries althought the complete transformation is known for the former [1] whereas in gravity we solve for the first few orders in an expansion. As an explicit application the one loop UV divergences of Hilbert-Einstein gravity with a cosmological constant and spin 0, 1/2 and 1 matter are computed with functional methods and in a field-covariant formalism.