Quantum-SpacetimeSymmetries: A Principle of Minimum Group Representation

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantumspacetime: this is the principle of minimal group representation, which allows us to consistently and simultaneously obtain a natural description of spacetime's dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the metaplectic group Mp(n), the double covering of SL(2C) in a vector representation, with respect to the coherent states carrying the spin weight. Our main results are[1]: