1997/03/09 by A. Chervov, Chervov, Alexander
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.q-alg/9703017
openalex publication_date 1997/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.