Hamiltonian structure of Dubrovin's equation of associativity in 2-d topological field theory

A third order Monge-Ampere type equation of associativity that Dubrovin has obtained in 2-d topological field theory is formulated in terms of a variational principle subject to second class constraints. Using Dirac's theory of constraints this degenerate Lagrangian system is cast into Hamiltonian form and the Hamiltonian operator is obtained from the Dirac bracket. There is a new type of KacMoody algebra that corresponds to this Hamiltonian operator. In particular, it is not a W-algebra. (C) 1996 American Institute of Physics.