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Quantization

In: Quantum Theory, Groups and Representations

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  • Peter Woit

    (Columbia University, Department of Mathematics)

Abstract

Given any Hamiltonian classical mechanical system with phase space $$\mathbf R^{2d}$$ , physics textbooks have a standard recipe for producing a quantum system, by a method known as “canonical quantization". We will see that for linear functions on phase space, this is just the construction we have already seen of a unitary representation $$\Gamma ^\prime _S$$ of the Heisenberg Lie algebra, the Schrödinger representation. The Stone–von Neumann theorem assures us that this is the unique such construction, up to unitary equivalence.

Suggested Citation

  • Peter Woit, 2017. "Quantization," Springer Books, in: Quantum Theory, Groups and Representations, chapter 0, pages 229-236, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-64612-1_17
    DOI: 10.1007/978-3-319-64612-1_17
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