Traces of creation-annihilation operators and Fredholm's formulas
q-alg
2008-02-03 v3 funct-an
High Energy Physics - Theory
Functional Analysis
Quantum Algebra
Abstract
We prove the formula for the traces of certain class of operators in bosonic and fermionic Fock spaces. Vertex operators belong to this class. Traces of vertex operators can be used for calculation of correlation functions and formfactors of integrable models (XXZ, Sine-Gordon, etc.), that is why we are interested in this problem. Also we show that Fredholm's minor and determinant can be expressed by such traces. We obtain a short proof of the Fredholm's formula for the solution of an integral equation. Analogue of Fredholm's formula in terms of permanents is obtained.
Keywords
Cite
@article{arxiv.q-alg/9703017,
title = {Traces of creation-annihilation operators and Fredholm's formulas},
author = {Alexander Chervov},
journal= {arXiv preprint arXiv:q-alg/9703017},
year = {2008}
}
Comments
20 pages, LaTex. Minor corrections