Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets

Details Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets Charged Free Fermions, Vertex Operators and Classical Theory of Conjugate Nets

1998-03-20

arxiv.org/abs/solv-int/9803015v1

J.Phys.A32:1197-1216,1999

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, 3 Postscript figures

Scientific paper

10.1088/0305-4470/32/7/010

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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