Dual S-matrix bootstrap. Part I. 2D theory
Andrea L. Guerrieri, Alexandre Homrich, Pedro Vieira
Abstract
A bstract Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems.
Topics & Concepts
PhysicsDuality (order theory)ObservableBootstrapping (finance)Dual (grammatical number)Convergence (economics)Theoretical physicsSymmetry (geometry)ScatteringApplied mathematicsMathematical physicsStrong dualityStatistical physicsScattering theoryBootstrap modelQuantum mechanicsDuality gapBound stateTensor decomposition and applicationsQuantum many-body systemsAlgebraic structures and combinatorial models