W. Kirwin

activity

20042019

most citedExtending coherent state transforms to Clifford analysis

20 citations · 48 across the 17 of their papers we have counts for

collaborators

Showing math.DGShow all

7 papers · 1 filter

math.DG2014★ 2 cited

Complex symplectomorphisms and pseudo-Kähler islands in the quantization of toric manifolds

William D. Kirwin, José M. Mourão, João P. Nunes

Let $P$ be a Delzant polytope. We show that the quantization of the corresponding toric manifold $X_{P}$ in toric Kähler polarizations and in the toric real polarization are relate…

math.DG2012★ 2 cited

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 $K$ , the pair $(K, C^{0} (K))$ has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this resul…

math.DG2012

Complex time evolution in geometric quantization and generalized coherent state transforms

William D. Kirwin, José M. Mourão, João P. Nunes

For the cotangent bundle $T^{*} K$ of a compact Lie group $K$ , we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert s…

math.DG2011

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…

math.DG2010★ 3 cited

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 $(X, ω)$ , such that $[ω /2 π] - c_{1} (X) /2 \in H^{2} (X, Z)$ and is nonnegative. We define the…

math.DG2010

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 $(M_{i}, g_{i}, ω_{i})$ ( $i = 1, 2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_i=\bigwedge^n…

math.DG2007★ 1 cited

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…