Abstract
Conserved quantities are obtained and analysed using new recently proposed models with global scale invariance. Such models allow for non-trivial scalar field potentials and masses for particles, so that the scale symmetry must somehow be broken. We obtain this conclusion by showing that the infrared behaviour of the conserved currents is singular so that there are no conserved charges associated with the global scale symmetry. Nevertheless, the scale symmetry plays a crucial role in determining the structure of the theory and it implies that in some high-field regions the potentials become flat.
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