Semiclassical geometry of integrable systems
Nicolai Reshetikhin
TL;DR
This paper derives a formula for the scalar product of semiclassical eigenvectors in integrable systems, with applications to asymptotics of Racah-Wigner coefficients, advancing understanding of semiclassical geometry.
Contribution
It introduces a new formula for scalar products of semiclassical eigenvectors in integrable systems, linking geometry with asymptotic analysis.
Findings
Derived a formula for scalar products of eigenvectors
Applied the formula to Racah-Wigner coefficient asymptotics
Enhanced understanding of semiclassical geometry in integrable systems
Abstract
The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application of this formula is the Ponzano-Regge type of asymptotic of Racah-Wigner coefficients.
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