Canonical commutation relations
Throughout this chapter (, ω) is a pre-symplectic space, that is, is a real vector space equipped with an anti-symmetric form ω. From the point of view of classical mechanics, will have the interpretation of the dual of a phase space, or, as we will say for brevity, of a dual phase space. Note that for quantum mechanics dual phase spaces seem more fundamental that phase spaces.
In this chapter we introduce ...