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… 
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  • C. Zachos
  • Physics
    International Journal of Modern Physics A
  • 2002
Wigner's quasi-probability distribution function in phase-space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear
...