# 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} }

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…

## 6 Citations

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We show how the tangent functor extends naturally from ordinary smooth maps to "microformal" (or "thick") morphisms of supermanifolds, a notion that we introduced earlier. Microformal morphisms…

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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…

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Microformal Geometry and Homotopy Algebras

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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

- Mathematics
- 2014

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…