Linear Symmetries of Scattering Amplitudes

If we define, roughly, linear symmetries as those symmetries which lead to linear relationships among scattering amplitudes, we are then faced with the question whether we already know all possible types of linear symmetries or whether there are new types of symmetries which we can yet discover. We argue that for an important class of these symmetries there can be no new types of symmetries, except for one which we call scaling symmetry. We also attempt to point out all types of symmetries which other classes have. In analyzing the above question we are led to a simple and consistent formalism for describing linear symmetries which takes linearity as the starting point for dealing with these symmetries. In this approach all linear symmetries are formally treated on an equal footing. General results on linear symmetries are derived: These symmetries are then classified into three main classes, and an effort is made to discover the characteristic properties of the individual classes.