# A differential Galois approach to path integrals

@article{MoralesRuiz2019ADG, title={A differential Galois approach to path integrals}, author={Juan Jos'e Morales-Ruiz}, journal={arXiv: Mathematical Physics}, year={2019} }

We point out the relevance of the Differential Galois Theory of linear differential equations for the exact semiclassical computations in path integrals in quantum mechanics. The main tool will be a necessary condition for complete integrability of classical Hamiltonian systems obtained by Ramis and myself : if a finite dimensional complex analytical Hamiltonian system is completely integrable with meromorphic first integrals, then the identity component of the Galois group of the variational… Expand

#### One Citation

Differential Galois Theory and Integration

- Mathematics
- Texts & Monographs in Symbolic Computation
- 2021

In this chapter, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods… Expand

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