Quantization of Forms on the Cotangent Bundle

@article{Voronov1999QuantizationOF,
  title={Quantization of Forms on the Cotangent Bundle},
  author={Theodore Th. Voronov},
  journal={Communications in Mathematical Physics},
  year={1999},
  volume={205},
  pages={315-336}
}
  • T. Voronov
  • Published 23 September 1998
  • Mathematics
  • Communications in Mathematical Physics
Abstract:We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on T⋆M is made into a space of (full) symbols of operators acting on forms on M. This gives rise to the composition of symbols, which is a deformation of the (“super”)commutative multiplication of forms. The symbol calculus is exact for differential operators and the symbols that are polynomial in momenta. We calculate the symbols of natural Laplacians. (Some nice Weitzenböck like… 
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