Resurgent deformation quantisation

@article{Garay2013ResurgentDQ,
  title={Resurgent deformation quantisation},
  author={Mauricio D. Garay and Axel Marcillaud de Goursac and Duco van Straten},
  journal={Annals of Physics},
  year={2013},
  volume={342},
  pages={83-102}
}

Figures from this paper

On the Moyal Star Product of Resurgent Series

We analyze the Moyal star product in deformation quantization from the resurgence theory perspective. By putting algebraic conditions on Borel transforms, one can define the space of

Hadamard Product and Resurgence Theory

We discuss the analytic continuation of the Hadamard product of two holomorphic functions under assumptions pertaining to Écalle’s Resurgence Theory, proving that if both factors are endlessly

Noncommutative Supergeometry and Quantum Supergroups

This is a review of concepts of noncommutative supergeometry - namely Hilbert superspace, C*-superalgebra, quantum supergroup - and corresponding results. In particular, we present applications of

Multipliers of Hilbert algebras and deformation quantization

In this paper, we introduce the notion of multiplier of a Hilbert algebra. The space of bounded multipliers is a seminite von Neumann algebra isomorphic to the left von Neumann algebra of the Hilbert

S-duality improved perturbation theory in compactified type I/heterotic string theory

A bstractWe study the mass of the stable non-BPS state in type I/heterotic string theory compactified on a circle with the help of the interpolation formula between weak and strong coupling results.

Degree Reduction in the Jacobian Conjecture, a Combinatorial Quantum Field Theoretical Approach

Let y=F(z) a polynomial system in C^n. The Jacobian Conjecture (JC) states that F is invertible, and its inverse is polynomial, if and only if the determinant of the Jacobian matrix J_F(z) = (d

Quantifications par déformations formelles et non formelles de la boule unité de C^n

A la frontiere de domaines de recherche tels que la geometrie differentielle, l’analyse harmonique sur les espaces homogenes, les equations aux derivees partielles ou la theorie des fonctions

Iterated convolutions and endless Riemann surfaces

We discuss a version of \'Ecalle's definition of resurgence, based on the notion of endless continuability in the Borel plane. We relate this with the notion of \Omega-continuability, where \Omega\

References

SHOWING 1-10 OF 40 REFERENCES

Deformation Quantization for Actions of R ]D

Oscillatory integrals The deformed product Function algebras The algebra of bounded operators Functoriality for the operator norm Norms of deformed deformations Smooth vectors, and exactness

Multi-instanton contributions in quantum mechanics

On the Stability under Convolution of Resurgent Functions

This article contains a self-contained proof of the stability under convolution of the class of resurgent functions associated with a closed discrete subset of C, under the assumption that , the set

Perturbative expansions in quantum mechanics

We prove a D = 1 analytic versal deformation theorem in the Heisenberg algebra. We define the spectrum of an element in the Heisenberg al- gebra. The quantised version of the Morse lemma already

Deformation quantization of Heisenberg manifolds

ForM a smooth manifold equipped with a Poisson bracket, we formulate aC*-algebra framework for deformation quantization, including the possibility of invariance under a Lie group of diffeomorphisms

Analytic Continuation of Eigenvalues of a Quartic Oscillator

We consider the Schrödinger operator on the real line with even quartic potential x4 + αx2 and study analytic continuation of eigenvalues, as functions of parameter α. We prove several properties of

The return of the quartic oscillator. The complex WKB method

The semi-classical treatment of the one-dimensional Schrodinger equation is made free from all approximation. For an analytic potential indeed, the WKB method in complex parameters can be formalized

On the stability by convolution product of a resurgent algebra

Various functional spaces take place in Resurgence theory : multiplicative spaces of formal series expansions that one would like to sum; convolutive spaces of analytic functions, the elements of