Self-adjointness of bound state operators in integrable quantum field theory
Yoh Tanimoto
August 26, 2015
We study self-adjoint extensions of operators which are the product of the
multiplication operator by an analytic function and the analytic continuation
in a strip. We compute the deficiency indices of the product operator for a
wide class of analytic functions. For functions of a particular form, we point
out the existence of a self-adjoint extension which is unitarily equivalent to
the analytic-continuation operation.
They appear in integrable quantum field theories as the one-particle
component of the operators which realize the bound states of elementary
particles and the existence of self-adjoint extension is a necessary step for
the construction of Haag-Kastler net for such models.
Keywords:
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