Quantum Mechanics for Mathematicians

For another treatment of these operators along the lines of this chapter, see
section 14 of [37].
For a concise but highly insightful discussion of the metaplectic representa-
tion, see chapters 16 and 17 in Graeme Segal’s section of [14]. For a discussion
of this topic emphasizing the role of the Fourier transform as an intertwining
operator, see [49]. The issue of the phase factor in the intertwining operators
and the metaplectic double cover will be discussed later in the context of the
harmonic oscillator, using a different realization of the Heisenberg Lie algebra
representation. For a discussion of this in terms of the Schr ̈odinger representa-
tion, see part I of [56].