Formal Groups and Conformal Field Theory over $\mathrm{Z}$

Abstract

We introduce a formal group naturally associated with algebraic curves. The formal group is isomorphic to the one obtained from the universal Witt scheme. The charge zero sector of the boson Fock space is regarded as the coordinate ring of the formal group. Using this structure, we can give tau functions. We also define new operators $f_n$, $v_n$ ($n \in \mathbf{Z}, n > 0$) on the fermion Fock space.