dorsal/arxiv
View SchemaCharged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets
| Authors | Adam Doliwa, Manuel Manas, Luis Martinez Alonso, Elena Medina, Paolo Maria Santini |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9803015 |
| URL | https://arxiv.org/abs/solv-int/9803015 |
| DOI | 10.1088/0305-4470/32/7/010 |
| Journal | J.Phys.A32:1197-1216,1999 |
Abstract
We show that the quantum field theoretical formulation of the $\tau$-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic vertex operators are Levy and adjoint Levy transformations and iii) the diagonal soliton vertex operators generate fundamental transformations. We also show that the bilinear identity for the multicomponent Kadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a bilinear identity for the multidimensional quadrilateral lattice equations.
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"abstract": "We show that the quantum field theoretical formulation of the $\\tau$-function\ntheory has a geometrical interpretation within the classical transformation\ntheory of conjugate nets. In particular, we prove that i) the partial charge\ntransformations preserving the neutral sector are Laplace transformations, ii)\nthe basic vertex operators are Levy and adjoint Levy transformations and iii)\nthe diagonal soliton vertex operators generate fundamental transformations. We\nalso show that the bilinear identity for the multicomponent\nKadomtsev-Petviashvili hierarchy becomes, through a generalized Miwa map, a\nbilinear identity for the multidimensional quadrilateral lattice equations.",
"arxiv_id": "solv-int/9803015",
"authors": [
"Adam Doliwa",
"Manuel Manas",
"Luis Martinez Alonso",
"Elena Medina",
"Paolo Maria Santini"
],
"categories": [
"solv-int",
"hep-th",
"math.DG",
"nlin.SI"
],
"doi": "10.1088/0305-4470/32/7/010",
"journal_ref": "J.Phys.A32:1197-1216,1999",
"title": "Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets",
"url": "https://arxiv.org/abs/solv-int/9803015"
},
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