6533b7defe1ef96bd12768bf

RESEARCH PRODUCT

Scattering on Riemannian Symmetric Spaces and Huygens Principle

Michael Semenov-tian-shanskyMichael Semenov-tian-shansky

subject

PhysicsScattering010102 general mathematicsStatistical and Nonlinear Physics16. Peace & justiceWave equation01 natural sciencesHuygens–Fresnel principlesymbols.namesakeRiemann hypothesis[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencessymbols010307 mathematical physicsScattering theory0101 mathematicsLink (knot theory)Mathematical PhysicsMathematical physics

description

International audience; The famous paper by L. D. Faddeev and B. S. Pavlov (1972) on automorphic wave equation explored a highly romantic link between Scattering Theory (in the sense of Lax and Phillips) and Riemann hypothesis. An attempt to generalize this approach to general semisimple Lie groups leads to an interesting evolution system with multidimensional time explored by the author in 1976. In the present paper, we compare this system with a simpler one defined for zero curvature symmetric spaces and show that the Huygens principle for this system in the curved space holds if and only if it holds in the zero curvature limit.

10.1142/s0129055x18400159https://hal.archives-ouvertes.fr/hal-01900077