The Space of Local Fields as a Module over the Ring of Local Integrals of Motion

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The chiral space of local fields in Sine-Gordon or the SU(2)-invariant Thirring model is studied as a module over the commutative algebra D of local integrals of motion. Using the recent construction of form factors by means of quantum affine algebra at root of unity due to Feigin et al. we construct a D-free resolution of the space of local fields. In general the cohomologies of the de Rham type complex associated with the space of local fields are determined and shown to be the irreducible representations of the symplectic group Sp(2∞). Babelon-Bernard-Smirnov's description of the space of local fields automatically incorporated in this framework.