scholarly journals Classical and quantum integrable systems in 263-1263-1263-1and separation of variables

1995 ◽  
Vol 172 (2) ◽  
pp. 263-285 ◽  
Author(s):  
J. Harnad ◽  
P. Winternitz
Keyword(s):  
Integrable Systems ◽  
Separation Of Variables ◽  
Quantum Integrable Systems

scholarly journals Separation of variables in AdS/CFT: functional approach for the fishnet CFT

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Andrea Cavaglià ◽  
Nikolay Gromov ◽  
Fedor Levkovich-Maslyuk
Keyword(s):  
Integrable Systems ◽  
Density Operator ◽  
Numerical Evaluation ◽  
Lagrangian Density ◽  
Separation Of Variables ◽  
Functional Approach ◽  
Quantum Integrable Systems ◽  
Arbitrary State ◽  
Nontrivial Coupling ◽  
The One

Abstract The major simplification in a number of quantum integrable systems is the existence of special coordinates in which the eigenstates take a factorised form. Despite many years of studies, the basis realising the separation of variables (SoV) remains unknown in $$ \mathcal{N} $$ N = 4 SYM and similar models, even though it is widely believed they are integrable. In this paper we initiate the SoV approach for observables with nontrivial coupling dependence in a close cousin of $$ \mathcal{N} $$ N = 4 SYM — the fishnet 4D CFT. We develop the functional SoV formalism in this theory, which allows us to compute non-perturbatively some nontrivial observables in a form suitable for numerical evaluation. We present some applications of these methods. In particular, we discuss the possible SoV structure of the one-point correlators in presence of a defect, and write down a SoV-type expression for diagonal OPE coefficients involving an arbitrary state and the Lagrangian density operator. We believe that many of the findings of this paper can be applied in the $$ \mathcal{N} $$ N = 4 SYM case, as we speculate in the last part of the article.

scholarly journals ALGEBRAIC ASPECT AND CONSTRUCTION OF LAX OPERATORS IN QUANTUM INTEGRABLE SYSTEMS

1995 ◽  
Vol 10 (40) ◽  
pp. 3113-3117 ◽  
Author(s):  
B. BASU-MALLICK ◽  
ANJAN KUNDU
Keyword(s):  
Integrable Systems ◽  
Integrable Models ◽  
Quantum Integrable Systems ◽  
Algebraic Construction ◽  
Algebraic Aspect ◽  
Quantum Integrable Models

An algebraic construction which is more general and closely connected with that of Faddeev,1 along with its application for generating different classes of quantum integrable models is summarized to complement the recent results of Ref. 1.

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