Abstract
The quantum theory of a free particle is intimately connected to the representation theory of the group of symmetries of space and time. This is well known for relativistic theories, where it is the representation theory of the Poincare group that is relevant, a topic that will be discussed in chapter 42. It is less well known that even in the non-relativistic case, the Euclidean group E(3) of symmetries of space plays a similar role, with irreducible representations of E(3) corresponding to free particle quantum theories for a fixed value of the energy.
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