In the first order form, the model considered by Strobl presents, besides local Lorentz and diffeomorphism invariances, an additional local non-linear symmetry. When the model is realized as a Poincar\'e gauge theory according to the procedure outlined in Refs.[1,2], the generators of the non-linear symmetry are responsible for the ``nasty constraint algebra''. We show that not only the Poincar\'e gauge theoretic formulation of the model is not the cause of the emerging of the undesirable constraint algebra, but actually allows to overcome the problem. In fact one can fix the additional symmetry without breaking the Poincar\'e gauge symmetry and the diffeomorphisms, so that, after a preliminary Dirac procedure, the remaining constraints uniquely satisfy the Poincar\'e algebra. After the additional symmetry is fixed, the equations of motion are unaltered. The objections to our method raised by Strobl in Ref.[3] are then immaterial. Some minor points put forward in Ref.[3] are also discussed.

Nardelli, G., Grignani, G., Reply to 'Comment on' gravity and the Poincare group', <<PHYSICAL REVIEW D>>, 1993; 1993 (D48): 5032-5035. [doi:10.1103/PhysRevD.48.5032] [http://hdl.handle.net/10807/8565]

Reply to 'Comment on' gravity and the Poincare group'

Nardelli, Giuseppe;Grignani, Gianluca
1993

Abstract

In the first order form, the model considered by Strobl presents, besides local Lorentz and diffeomorphism invariances, an additional local non-linear symmetry. When the model is realized as a Poincar\'e gauge theory according to the procedure outlined in Refs.[1,2], the generators of the non-linear symmetry are responsible for the ``nasty constraint algebra''. We show that not only the Poincar\'e gauge theoretic formulation of the model is not the cause of the emerging of the undesirable constraint algebra, but actually allows to overcome the problem. In fact one can fix the additional symmetry without breaking the Poincar\'e gauge symmetry and the diffeomorphisms, so that, after a preliminary Dirac procedure, the remaining constraints uniquely satisfy the Poincar\'e algebra. After the additional symmetry is fixed, the equations of motion are unaltered. The objections to our method raised by Strobl in Ref.[3] are then immaterial. Some minor points put forward in Ref.[3] are also discussed.
Inglese
Nardelli, G., Grignani, G., Reply to 'Comment on' gravity and the Poincare group', <<PHYSICAL REVIEW D>>, 1993; 1993 (D48): 5032-5035. [doi:10.1103/PhysRevD.48.5032] [http://hdl.handle.net/10807/8565]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/8565
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