525 citations · 7.1k across the 109 of their papers we have counts for
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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…
Coherent states, quantum gravity and the Born-Oppenheimer approximation, III: Applications to loop quantum gravity
Alexander Stottmeister, Thomas Thiemann
In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space…
Coherent states, quantum gravity and the Born-Oppenheimer approximation, II: Compact Lie Groups
Alexander Stottmeister, Thomas Thiemann
In this article, the second of three, we discuss and develop the basis of a Weyl quantisation for compact Lie groups aiming at loop quantum gravity-type models. This Weyl quantisat…
Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
Alexander Stottmeister, Thomas Thiemann
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum syst…