Non-formal Rankin-Cohen deformation
(2018)
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- Authors
- Supervisors
- Bieliavsky, Pierre
- Abstract
- In classical mechanics, the space of observables of a dynamical system constitutes a commutative algebra of smooth functions on a symplectic manifold. In quantum mechanics, things are different: at that level, the observables form a noncommutative algebra of linear operators acting on a Hilbert space. The theory of formal deformation quantization proposes to realize the quantization of a classical system as a formal associative one-parameter deformation of the pointwise product of functions in the direction of the Poisson bracket of the classical system. In the framework of non-formal deformation quantization, one seeks to convergent deformation quantizations in the sense that the deformed product of two functions is again a function rather than a formal power series with coefficients in the smooth functions. This work consists in the construction of a non-formal deformation quantization which is a convergent version of Zagier’s Rankin-Cohen deformation on modular forms.
- Affiliations
Citations
Dendoncker, V. (2018). Non-formal Rankin-Cohen deformation. https://hdl.handle.net/2078.5/126380