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It is shown how the different irreducibility classes of the energy-momentumtensor allow for a Lagrangian formulation of the gravity-matter system using aselfdual 2-form as a basic variable. It is pointed out what kind ofdifficulties arise when attempting to construct a pure spin-connectionformulation of the gravity-matter system. Ambiguities in the formulationespecially concerning the need for constraints are clarified.Comment: title changed, extended versio

Self-dual 2-form formulation of gravity and classification of energy - momentum tensors