We introduce the field algebra Σ D ( M ; n ⊗ n g ) associated with the current algebra D r ( M ; g ) for the Lie algebra g over physical space M . The Heisenberg magnet model is generalized to this continuum. It is shown that the Hamiltonian can be given meaning as implementing a derivation of the field algebra in certain representations. We introduce new representations of the current algebra. For example, if G = SU(2), a representation in L 2( R 3)⊗ 3 is [σ(ƒ) F] j = ε jkl ϕ k ψ l for (ϕ k ) = ƒ in D r ( M ; g )(ψ l = F. This has cyclic subrepresentations with prime parts.