dorsal/arxiv
View SchemaTraces of creation-annihilation operators and Fredholm's formulas
| Authors | Alexander Chervov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9703017 |
| URL | https://arxiv.org/abs/q-alg/9703017 |
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.
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"date_created": "2026-03-02T18:01:28.003000Z",
"date_modified": "2026-03-02T18:01:28.003000Z",
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"abstract": "We prove the formula for the traces of certain class of operators in bosonic\nand fermionic Fock spaces. Vertex operators belong to this class. Traces of\nvertex operators can be used for calculation of correlation functions and\nformfactors of integrable models (XXZ, Sine-Gordon, etc.), that is why we are\ninterested in this problem. Also we show that Fredholm\u0027s minor and determinant\ncan be expressed by such traces. We obtain a short proof of the Fredholm\u0027s\nformula for the solution of an integral equation. Analogue of Fredholm\u0027s\nformula in terms of permanents is obtained.",
"arxiv_id": "q-alg/9703017",
"authors": [
"Alexander Chervov"
],
"categories": [
"q-alg",
"funct-an",
"hep-th",
"math.FA",
"math.QA"
],
"title": "Traces of creation-annihilation operators and Fredholm\u0027s formulas",
"url": "https://arxiv.org/abs/q-alg/9703017"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "f0296ce9-8ebd-4e03-882d-4b1e861db046",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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