• Corpus ID: 119661351

# Quantum microformal morphisms of supermanifolds: an explicit formula and further properties

@article{Voronov2015QuantumMM,
title={Quantum microformal morphisms of supermanifolds: an explicit formula and further properties},
author={Theodore Th. Voronov},
journal={arXiv: Mathematical Physics},
year={2015}
}
• T. Voronov
• Published 14 December 2015
• Mathematics
• arXiv: Mathematical Physics
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier integral operators of a particular kind. They act on oscillatory wave functions, whose algebra extends the algebra of formal power series in Planck's constant. In the classical limit, quantum microformal morphisms reproduce, as the main term of the asymptotic…
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• T. Voronov
• Mathematics
Proceedings of the Steklov Institute of Mathematics
• 2018
We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal, or “thick,” morphisms. They are formal canonical relations of a special form, constructed

## References

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Thick morphisms of supermanifolds and oscillatory integral operators
We show that thick morphisms (or microformal morphisms) between smooth (super)manifolds, introduced by us before, are classical limits of 'quantum thick morphisms' defined here as particular
The "nonlinear pullback" of functions and a formal category extending the category of supermanifolds
We introduce mappings between function spaces on smooth (super)manifolds, which are generally nonlinear and which generalize the pullbacks with respect to smooth maps. The construction uses canonical