Michio Jimbo,Tetsuji Miwa,Fedor Smirnov
Local Operators in Integrable Models I
Local Operators in Integrable Models I
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Excellent- More about Local Operators in Integrable Models I
This book is the first published monograph on the space of local operators in integrable lattice models, treating the six-vertex model and the XXZ Heisenberg spin chain. It uses a pair of fermions to create a basis of the space of local operators, leading to the expression of all correlation functions in terms of two transcendental functions with rational coefficients. Step-by-step explanations are provided for all materials necessary for this construction, with examples and applications given along with numerical results.
Format: Paperback / softback
Length: 192 pages
Publication date: 01 July 2021
Publisher: American Mathematical Society
A rich and intricate research domain at the confluence of contemporary mathematics and theoretical physics is formed by integrable models in statistical mechanics and quantum field theory. Understanding the space of local operators within the system and, ultimately, their correlation functions and form factors is a crucial concern. This book stands as the inaugural published monograph on this subject, delving into the realm of integrable lattice models, particularly focusing on the six-vertex model and the XXZ Heisenberg spin chain. A fundamental aspect of this exploration involves introducing a pair of fermions to establish a basis for the space of local operators. This leads to the remarkable result that all correlation functions at finite distances can be expressed in terms of two transcendental functions with rational coefficients. Step-by-step explanations are provided for all the necessary materials, encompassing algebraic Bethe ansatz, representations of quantum groups, the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory, Riemann surfaces, and their Jacobians. Numerous examples and applications are showcased, accompanied by numerical results, making this book an invaluable resource for readers seeking to delve into the forefront of this rapidly evolving research field.
Weight: 378g
Dimension: 255 x 181 x 13 (mm)
ISBN-13: 9781470465520
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