Charged free fermions, vertex operators and the classical theory of conjugate nets
| Autor: | Paolo Maria Santini, Luis Martínez Alonso, Manuel Manas, Elena Medina, Adam Doliwa |
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| Rok vydání: | 1999 |
| Předmět: |
High Energy Physics - Theory
Mathematics - Differential Geometry Pure mathematics Quadrilateral Nonlinear Sciences - Exactly Solvable and Integrable Systems Laplace transform Diagonal FOS: Physical sciences General Physics and Astronomy Bilinear interpolation Statistical and Nonlinear Physics Fermion Partial charge Nonlinear Sciences::Exactly Solvable and Integrable Systems High Energy Physics - Theory (hep-th) Differential Geometry (math.DG) Lattice (order) FOS: Mathematics Exactly Solvable and Integrable Systems (nlin.SI) Quantum field theory Mathematical Physics Mathematics |
| Zdroj: | Journal of Physics A: Mathematical and General. 32:1197-1216 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/32/7/010 |
| Popis: | 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. Comment: 28 pages, 3 Postscript figures |
| Databáze: | OpenAIRE |
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