Unitarity of the SoV Transform for $\mathrm{SL}(2,\mathbb{C})$ Spin Chains

Abstract

We prove the unitarity of the separation of variables transform for $\mathrm{SL}(2,\mathbb{C})$ spin chains by a method based on the use of Gustafson integrals.

References in corpus (19)

• High energy QCD as a completely integrable model
• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Quantum Inverse Scattering Method. Selected Topics
• Noncompact Heisenberg spin magnets from high-energy QCD: I. Baxter Q-operator and Separation of Variables
• Baxter's Q-operator for the homogeneous XXX spin chain
• Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
• Integrability of scattering amplitudes in N=4 SUSY
• Integral representations for the eigenfunctions of quantum open and periodic Toda chains from QISM formalism
• Exactly solvable magnet of conformal spins in four dimensions
• Separation of variables for rational gl(n) spin chains in any compact representation, via fusion, embedding morphism and Backlund flow
• Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet
• Integrable spin chains and scattering amplitudes
• On Complex Gamma-Function Integrals
• On quantum separation of variables beyond fundamental representations
• Form-factors and complete basis of observables via separation of variables for higher rank spin chains
• On the separation of variables for the modular XXZ magnet and the lattice Sinh-Gordon models
• Integrable systems, separation of variables and the Yang-Baxter equation
• Completeness of SoV Representation for $\mathrm{SL}(2,\mathbb{R})$ Spin Chains

Cited by in corpus (1)

• BC-type open $SL(2,\mathbb{C})$ spin chain