Physically Relevant Representations

Abstract

From the examples and the discussion of the previous chapter, it appears that for infinite systems the choice of the representation for the algebra of canonical variables (a basic preliminary step for even defining the dynamical problem) is a highly non-trivial problem (unless the model is exactly soluble). Among the possible representations of the relevant algebra $\mathcal{A}$, it is therefore convenient to isolate those which are physically acceptable. For the moment, we restrict our discussion to the zero temperature case. The non-zero temperature case will be briefly discussed in Chap. 12. On the basis of general physical considerations, we require the following conditions for a physically relevant representation π.