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A categorical framework for the quantum harmonic oscillator

Abstract:

This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely general one in which Hilbert spaces play no special role. Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates of the lowering operators. Surprisingly, generalised expon...

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Journal:
International Journal of Theoretical Physics
Volume:
47
Issue:
12
Pages:
3408-3447
Publication date:
2008-01-01
URN:
uuid:7759368d-cbe2-440f-ae9f-39db4626dd6d
Local pid:
cs:2882

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