the formalism of quantum mechanics specified by covariance properties

L. Ferrari

Wanda Hanus

Giuseppe Nisticò, Luigi Accardi, Guillaume Adenier +5 more

The known methods, due for instance to G.W. Mackey and T.F. Jordan, which exploit the transformation properties with respect to the Euclidean and Galileian group to determine the formalism of the Quantum Theory of a localizable particle, fail in the case that the considered transformations are not symmetries of the physical system. In the present work we show that the formalism of standard Quantum Mechanics for a particle without spin can be completely recovered by exploiting the covariance properties with respect to the group of Euclidean transformations, without requiring that these transformations are symmetries of the physical system.

Wayne Nicholas Polyzou

It is shown that the assumptions of Poincar\'e invariance and manifest covariance in quantum mechanics requires an interaction-dependent scalar product. Properties of the kernel of the inner product based on these assumptions are derived. Additional assumptions further restrict the form of this kernel. The relationship of this result to local quantum field theory and covariant constraint dynamics is discussed. A formal representation of a kernel satisfying all of these properties is given in terms of two-body constraints.

Sol Wieder