The Metaplectic Representation and Annihilation and Creation Operators, $$d=1$$

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

Chapter Chapter 24 in Quantum Theory, Groups and Representations, 2017, pp 313-324 from Springer

Abstract: Abstract In section 22.4 , we saw that annihilation and creation operators quantize complexified coordinate functions $${\overline{z}}, z$$ on phase space, giving a representation of the complexified Heisenberg Lie algebra $$\mathfrak h_3\otimes \mathbf C$$ . In this chapter, we will see what happens for quadratic combinations of the $${\overline{z}}, z$$ , which after quantization give quadratic combinations of the annihilation and creation operators.

Date: 2017
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DOI: 10.1007/978-3-319-64612-1_24

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