20 citations · 48 across the 17 of their papers we have counts for
19 papers
Holomorphic fractional Fourier transforms
William D. Kirwin, José Mourão, João P. Nunes +1
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Trans…
Segal-Bargmann transforms from hyperbolic Hamiltonians
William D. Kirwin, José Mourão, João P. Nunes +1
We consider the imaginary time flow of a quadratic hyperbolic Hamiltonian on the symplectic plane, apply it to the Schrödinger polarization and study the corresponding evolution of…
Extending coherent state transforms to Clifford analysis
William D. Kirwin, José Mourão, João P. Nunes +1
We introduce two extensions of the Segal-Bargmann coherent state transform from to Hilbert spaces of slice monogenic and axial monogenic functions and study t…
Complex symplectomorphisms and pseudo-Kähler islands in the quantization of toric manifolds
William D. Kirwin, José M. Mourão, João P. Nunes
Let be a Delzant polytope. We show that the quantization of the corresponding toric manifold in toric Kähler polarizations and in the toric real polarization are relate…
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…
Coherent state transforms and the Mackey-Stone-Von Neumann theorem
William D. Kirwin, José M. Mourão, João P. Nunes
Mackey showed that for a compact Lie group , the pair has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this resul…
Complex time evolution in geometric quantization and generalized coherent state transforms
William D. Kirwin, José M. Mourão, João P. Nunes
For the cotangent bundle of a compact Lie group , we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert s…
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…
Classical Equivalence and Quantum Equivalence of Magnetic Fields on Flat Tori
Carolyn Gordon, William Kirwin, Dorothee Schueth +1
Let M be a real 2m-torus equipped with a translation-invariant metric h and a translation-invariant symplectic form w; the latter we interpret as a magnetic field on M. The Hamilto…
Degeneration of Kaehler structures and half-form quantization of toric varieties
William D. Kirwin, José M. Mourão, João P. Nunes
We study the half-form Kaehler quantization of a smooth symplectic toric manifold , such that and is nonnegative. We define the…
Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent
Carolyn Gordon, William D. Kirwin, Dorothee Schueth +1
We construct pairs of compact Kähler-Einstein manifolds ( of complex dimension with the following properties: The canonical line bundle $L_i=\bigwedge^n…
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…
Higher Asymptotics of Laplace's Approximation
William D. Kirwin
We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation)…
Theta-functions on the Kodaira-Thurston manifold
William D. Kirwin, Alejandro Uribe
The Kodaira--Thurston M manifold is a compact, 4-dimensional nilmanifold which is symplectic and complex but not Kaehler. We describe a construction of theta-functions associated t…
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…