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Mathematics of Quantization and Quantum Fields by Christian Gérard, Jan Derezinski

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8

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 ...

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