p-adic angular momentum coupling in symplectic geometry

2025/10/15 by Luis Crespo, Crespo, Luis, Álvaro Pelayo +1
Mathematics · #37P05 #53D20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2510.13415

openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

The coupled angular momentum is an integrable system with two degrees of freedom which is fundamental in physics and the theory of integrable systems. It is obtained by coupling two angular momenta. We construct a p-adic analog of this system for any prime number p and describe its symplectic normal forms at the critical points. This analog has a rich singularity theory with up to thirteen non-equivalent symplectic normal forms, which stands in contrast with the real case where there are exactly three normal forms.

Citations

• Integrable systems with symmetries: toric, semitoric, and beyond
• Darboux's Theorem in p-adic symplectic geometry
• Rigidity and flexibility in p-adic symplectic geometry
• p-adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I
• Symplectic invariants of semitoric systems and the inverse problem for\n quantum systems
• Convexity of singular affine structures and toric-focus integrable Hamiltonian systems
• Hamiltonian and symplectic symmetries: an introduction
• Symplectic geometry and spectral properties of classical and quantum coupled angular momenta
• Symplectic group and Heisenberg group in p-adic quantum mechanics
• Multifractals, Mumford curves, and Eternal Inflation
• Voevodsky's Univalence Axiom in homotopy type theory
• Homotopy type theory and Voevodsky's univalent foundations
• Constructing integrable systems of semitoric type
• p-Adic and Adelic Quantum Mechanics
• Symplectic Geometry

Cited by

• Darboux's Theorem in p-adic symplectic geometry

Related

• Symplectic geometry and spectral properties of classical and quantum coupled angular momenta
• The p-adic Jaynes-Cummings model in symplectic geometry
• p-adic symplectic geometry of integrable systems and Weierstrass-Williamson theory I
• Symplectic integrators and the conservation of angular momentum
• Norm-squared of the momentum map in infinite dimensions with applications to Kähler geometry and symplectic connections