A differential Galois approach to path integrals

DOI10.1063/1.5134859zbMath1443.81051arXiv1910.06365OpenAlexW3098149588MaRDI QIDQ3298942

Juan J. Morales-Ruiz

Publication date: 16 July 2020

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.06365

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items (2)

Semiclassical quantification of some two degree of freedom potentials: A differential Galois approach ⋮ Differential Galois Theory and Integration

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Picard-Vessiot theory and integrability
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Galoisian obstructions to non-Hamiltonian integrability
• Galoisian obstructions to integrability of Hamiltonian systems. II.
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• Handbook of Feynman path integrals
• Galoisian obstructions to integrability of Hamiltonian systems. I.
• A note on the non-integrability of some Hamiltonian systems with a homogeneous potential.
• From the Peierls bracket to the Feynman functional integral
• Simple explicit formulas for Gaussian path integrals with time-dependent frequencies
• Feynman's path integral. Definition without limiting procedure
• Functional integration
• Liouvillian propagators, Riccati equation and differential Galois theory
• Differential Galois Theory through Riemann-Hilbert Correspondence
• Picard-Vessiot Extensions of Real Differential Fields
• Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
• Functional determinants in quantum field theory
• Semiclassical Mechanics
• Liouvillian Propagators and Degenerate Parametric Amplification with Time-Dependent Pump Amplitude and Phase
• Functional Integration
• Differential Galois theory and non-integrability of Hamiltonian systems
• Some questions looking for answers in dynamical systems

This page was built for publication: A differential Galois approach to path integrals