1,044 research outputs found
The determinant representation for quantum correlation functions of the sinh-Gordon model
We consider the quantum sinh-Gordon model in this paper. Using known formulae
for form factors we sum up all their contributions and obtain a closed
expression for a correlation function. This expression is a determinant of an
integral operator. Similar determinant representations were proven to be useful
not only in the theory of correlation functions, but also in the matrix models.Comment: 21 pages, Latex, no figure
A Compact Formula for Rotations as Spin Matrix Polynomials
Group elements of SU(2) are expressed in closed form as finite polynomials of
the Lie algebra generators, for all definite spin representations of the
rotation group. The simple explicit result exhibits connections between group
theory, combinatorics, and Fourier analysis, especially in the large spin
limit. Salient intuitive features of the formula are illustrated and discussed
Exactly solvable dynamical systems in the neighborhood of the Calogero model
The Hamiltonian of the -particle Calogero model can be expressed in terms
of generators of a Lie algebra for a definite class of representations.
Maintaining this Lie algebra, its representations, and the flatness of the
Riemannian metric belonging to the second order differential operator, the set
of all possible quadratic Lie algebra forms is investigated. For N=3 and N=4
such forms are constructed explicitly and shown to correspond to exactly
solvable Sutherland models. The results can be carried over easily to all .Comment: 23 pages, 2 figures, replaced and enlarged versio
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