Ultimately our fundamental goal in particle physics is to understand the dynamics, i.e. to have a theory from which we can actually calculate transition amplitudes. Tests of the theory will involve, at the crudest level, measurements of differential cross-sections or decay rates but, at a more sophisticated and more probing level, measurements of all kinds of spindependent phenomena. On the one hand, given a dynamical theory it is probably simplest to calculate the helicity transition amplitudes and from them the formulae for the spin-dependent observables that can be tested against experimental data. On the other hand, in the absence of a theory it would seem best to try to obtain information on the behaviour of the transition amplitudes from a sufficiently large number of different independent measurements. In this way one would hope to be led to deduce the nature of the underlying dynamics.

In both these situations it is important to bear in mind that certain properties are intrinsic to transition amplitudes, i.e. they do not depend upon detailed dynamical theory but rather follow from very general conservation laws, principally from the conservation of angular momentum.

The study of reactions thus divides into two phases:

1. (1) the general properties of transition amplitudes and the connection between their behaviour and the underlying dynamics; and

2. (2) the relationship between transition amplitudes and observables.

In this chapter we concentrate upon the former. The latter will be discussed in Chapter 5.