Integrable models in statistical mechanics and quantum field theory
constitute a rich research field at the crossroads of modern
mathematics and theoretical physics. An important issue to
understand is the space of local operators in the system and,
ultimately, their correlation functions and form factors. This book
is the first published monograph on this subject. It treats
integrable lattice models, notably the six-vertex model and the XXZ
Heisenberg spin chain. A pair of fermions is introduced and used to
create a basis of the space of local operators, leading to the
result that all correlation functions at finite distances are
expressible in terms of two transcendental functions with rational
coefficients. Step-by-step explanations are given for all materials
necessary for this construction, ranging from algebraic Bethe
ansatz, representations of quantum groups, and the
Bazhanov-Lukyanov-Zamolodchikov construction in conformal field
theory to Riemann surfaces and their Jacobians. Several examples
and applications are given along with numerical results. Going
through the book, readers will find themselves at the forefront of
this rapidly developing research field.
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