1207.6787 (Stephen G. Low)

Maximal quantum mechanical symmetry: Projective representations of the
Weyl-Heisenberg automorphism group    [PDF]

Stephen G. Low

The Heisenberg commutation relations are fundamental to quantum mechanics. Consider a symmetry group and its projective representations transforming quantum physical states. The Heisenberg commutation relations must be valid in the original and in the transformed states. This paper determines the maximal symmetry group and the projective representations acting on the quantum physical states that so that the Heisenberg commutation relations are valid in all the transformed states. Any symmetry that is physical in the sense that it preserves the Heisenberg commutation relations must be a subgroup and its projective representations must be contained in the above maximal symmetry representations.

View original: http://arxiv.org/abs/1207.6787