20 citations · 48 across the 17 of their papers we have counts for
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Quantizing the geodesic flow via adapted complex structures
William D. Kirwin
The geometric quantization of the geodesic flow on a compact Riemannian manifold via the BKS "dragging projection" yields the Laplacian plus a scalar curvature term. To avoid conve…
Complex structures adapted to magnetic flows
Brian C. Hall, William D. Kirwin
Let be a compact real-analytic manifold, equipped with a real-analytic Riemannian metric and let be a closed real-analytic 2-form on , interpreted as a magnetic fie…
Isotropic foliations of coadjoint orbits from the Iwasawa decomposition
William D. Kirwin
Let G be a noncompact real semisimple Lie group. The regular coadjoint orbits of G can be partitioned into a finite set of types. We show that on each regular orbit, the Iwasawa de…
Adapted complex structures and the geodesic flow
Brian C. Hall, William D. Kirwin
In this paper, we give a new construction of the adapted complex structure on a neighborhood of the zero section in the tangent bundle of a compact, real-analytic Riemannian manifo…
Higher Asymptotics of Unitarity in "Quantization Commutes with Reduction"
William D. Kirwin
Let M be a compact Kaehler manifold equipped with a Hamiltonian action of a compact Lie group G. In [Invent. Math. 67 (1982), no.~3, 515--538], Guillemin and Sternberg showed that…
Unitarity in "quantization commutes with reduction"
Brian C. Hall, William D. Kirwin
Let M be a compact Kahler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M//G.…
Coherent States in Geometric Quantization
William D. Kirwin
In this paper we study overcomplete systems of coherent states associated to compact integral symplectic manifolds by geometric quantization. Our main goals are to give a systemati…
Geometric Quantization, Parallel Transport and the Fourier Transform
William D. Kirwin, Siye Wu
In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of g…