ABSTRACT
M and P are ready to construct a model for position and momentum in three dimensions. Their strategy is to generalize their one-dimensional model step-by-step. M begins with a definition that amounts to “forgetting the origin” of the oriented inner product space (V, 〈, 〉) of Chapter 1, thereby allowing for the possibility that M and P may be at different locations in physical space.
Definition 8.1. Physical space is a real affine space, A3, of dimension 3. More precisely, the set A3 is endowed with a simply transitive action of the underlying Lie group (V,+) of a three-dimensional oriented real inner product space (V, 〈, 〉):
