# Abelian gerbes as a gauge theory of quantum mechanics on phase space

@article{Isidro2006AbelianGA, title={Abelian gerbes as a gauge theory of quantum mechanics on phase space}, author={Jos{\'e} Maria Isidro and Maurice A. de Gosson}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2006}, volume={40}, pages={3549 - 3567} }

We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space . The connection is given by a triple of forms A, B, H: a potential 1-form A, a Neveu–Schwarz potential 2-form B, and a field-strength 3-form H = dB. All three of them are defined exclusively in terms of elements already present in , the only external input being Planck's constant ℏ. U(1) gauge transformations acting on the triple A, B, H are also defined, parametrized either by a 0-form or by a 1-form…

## 5 Citations

### Phase-Space Weyl Calculus and Global Hypoellipticity of a Class of Degenerate Elliptic Partial Differential Operators

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In a recent series of papers M.W. Wong has studied a degenerate elliptic partial differential operator related to the Heisenberg group. It turns out that Wong’s example is best understood when…

### Semi-classical propagation of wavepackets for the phase space Schrödinger equation: interpretation in terms of the Feichtinger algebra

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The nearby orbit method is a powerful tool for constructing semi-classical solutions of Schrodinger's equation when the initial datum is a coherent state. In this paper, we first extend this method…

### Semi-classical propagation of wavepackets for the phase space Schrödinger equation: interpretation in terms of the Feichtinger algebra

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The nearby orbit method is a powerful tool for constructing semi-classical solutions of Schrödinger's equation when the initial datum is a coherent state. In this paper, we first extend this method…

### On the noncommutative eikonal

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- 2010

We study the Eikonal approximation to quantum mechanics on the Moyal plane. Instead of using a star product, the analysis is carried out in terms of operator-valued wavefunctions depending on…

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