Baxter Bbb Q-operator and separation of variables for the open SL(2,Bbb R) spin chain | Zendy

S. É. Derkachov | Zendy; G.P. Korchemsky | Zendy; A. N. Manashov | Zendy

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Baxter Bbb Q-operator and separation of variables for the open SL(2,Bbb R) spin chain

Author(s) -

S. É. Derkachov,

G.P. Korchemsky,

A. N. Manashov

Publication year - 2003

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2003/10/053

Subject(s) - integrable system , operator (biology) , separation of variables , eigenvalues and eigenvectors , mathematics , spin (aerodynamics) , chain (unit) , pure mathematics , kernel (algebra) , mathematical physics , quantum , measure (data warehouse) , physics , quantum mechanics , mathematical analysis , chemistry , computer science , repressor , transcription factor , gene , thermodynamics , database , boundary value problem , biochemistry

We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL(2,R) and SL(2,C) spin chains

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