# Multi-instantons and exact results I: Conjectures, WKB expansions, and instanton interactions

@article{ZinnJustin2004MultiinstantonsAE, title={Multi-instantons and exact results I: Conjectures, WKB expansions, and instanton interactions}, author={Jean Zinn-Justin and Ulrich D. Jentschura}, journal={Annals of Physics}, year={2004}, volume={313}, pages={197-267} }

## Figures and Tables from this paper

## 146 Citations

### Resurgence theory, ghost-instantons, and analytic continuation of path integrals

- Physics
- 2013

A bstractA general quantum mechanical or quantum field theoretical system in the path integral formulation has both real and complex saddles (instantons and ghost-instantons). Resurgent asymptotic…

### Quantum geometry of resurgent perturbative/nonperturbative relations

- Physics
- 2017

A bstractFor a wide variety of quantum potentials, including the textbook ‘instanton’ examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from…

### Resurgence in sine-Gordon quantum mechanics: exact agreement between multi-instantons and uniform WKB

- Physics
- 2015

A bstractWe compute multi-instanton amplitudes in the sine-Gordon quantum mechanics (periodic cosine potential) by integrating out quasi-moduli parameters corresponding to separations of instantons…

### Multi-instantons and exact results III: Unification of even and odd anharmonic oscillators

- Physics
- 2010

### Instanton Effects and Quantum Spectral Curves

- Physics, Mathematics
- 2013

We study a spectral problem associated to the quantization of a spectral curve arising in local mirror symmetry. The perturbative WKB quantization condition is determined by the quantum periods, or…

### Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves

- PhysicsJournal of High Energy Physics
- 2019

A bstractWe study the Harper-Hofstadter Hamiltonian and its corresponding non-perturbative butterfly spectrum. The problem is algebraically solvable whenever the magnetic flux is a rational multiple…

### Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: phi3 QFT in 6 Dimensions

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2021

We analyze the asymptotically free massless scalar φ quantum field theory in 6 dimensions, using resurgent asymptotic analysis to find the trans-series solutions which yield the non-perturbative…

## References

SHOWING 1-10 OF 40 REFERENCES

### Summation of divergent series by order dependent mappings: Application to the anharmonic oscillator and critical exponents in field theory

- Physics
- 1979

We study numerically a method of summation of divergent series based on an order dependent mapping. We consider the example of a simple integral, of the ground‐state energy of the anharmonic…

### Instantons in gauge theories

- Physics
- 1994

This volume is a compilation of works which, taken together, give a complete and consistent presentation of instanton calculus in non-Abelian gauge theories, as it exists now. Some of the papers…

### Expansion around instantons in quantum mechanics

- Physics
- 1981

We calculate numerically a few terms of the corrections to the large‐order behavior of the ground state energy of the O(N) anharmonic oscillator by analyzing the perturbation series. We then generate…

### Perturbation theory at large orders for a potential with degenerate minima

- Physics, Mathematics
- 1977

Perturbation theory at large orders for a potential with degenerate minima differs from other cases discussed in previous works. The pseudoparticle which interpolates between the two classical minima…

### Quantum field theory

- Physics
- 1956

This book is a modern pedagogic introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian…