32 citations · 55 across the 19 of their papers we have counts for
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A gauge theory of quantum mechanics
J. M. Isidro, M. A. de Gosson
An Abelian gerbe is constructed over classical phase space. The 2-cocycles defining the gerbe are given by Feynman path integrals whose integrands contain the exponential of the Po…
On a product formula for the Conley--Zehnder index of symplectic paths and its applications
Maurice de Gosson, Serge de Gosson, Paolo Piccione
Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley--Zehnder index of continuous paths…
Squeezed Coherent States and a Semiclassical Propagator for the Schroedinger equation in Phase
Maurice de Gosson, Serge de Gosson
We construct semiclassical solutions of the symplectically covariant Schroedinger phase-space equation rigorously studied in a previous paper; we use for this purpose an adaptation…
Symplectic Non-Squeezing Theorems, Quantization of Integrable Systems, and Quantum Uncertainty
Maurice De Gosson
The ground energy level of an oscillator cannot be zero because of Heisenberg's uncertainty principle. We use methods from symplectic topology (Gromov's non-squeezing theorem, and…