Quantization

Peter Woit ()
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Peter Woit: Columbia University, Department of Mathematics

Chapter Chapter 17 in Quantum Theory, Groups and Representations, 2017, pp 229-236 from Springer

Abstract: 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-64612-1_17

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DOI: 10.1007/978-3-319-64612-1_17

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