Abstract
Considerable progress has been made in the last decade in the elaboration of non perturbative methods allowing the exact resolution of a large class of two dimensional models in field theory and in statistical mechanics both at classical and quantum levels. Underlying these exiting developments of the notion of complete integrability in systems with an infinite number of degrees of freedom, the concept of new algebraic structures (The Yang-Baxter algebras and equations) has emerged[l]. In fact, these algebras usually provide us with the complete canonical structure of such models of field theory, leading in particular to an infinite set of conserved charges in involution, as a signature of the complete integrability.
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References
Surveys where many references to original works can be found are: L.D. Faddeev, in Les Houches Lectures (1982), Recent Advances in Field Theory & Statistical Mechanics, eds. J.B. Zuber & R. Stora (North Holland, 1984)., P.P. Kulish & E.K. Sklyanin, in Tvärmine Lectures, eds. J. Hietarinta & C. Montonen, Springer Lectures in Physics (1982) Vol. 151. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, 1982).
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© 1987 Plenum Press, New York
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Maillet, J.M. (1987). New Algebraic Canonical Structures Of Integrability In 2-D Field Theories. In: Lee, H.C., Elias, V., Kunstatter, G., Mann, R.B., Viswanathan, K.S. (eds) Super Field Theories. NATO Science Series, vol 160. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0913-0_30
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DOI: https://doi.org/10.1007/978-1-4613-0913-0_30
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