Continuous Space-time Symmetries in a Lattice Field Theory

For purposes of regularization as well as numerical simulation, the discretization of Lorentz invariant continuum field theories on a space-time lattice is often convenient. In general this discretization destroys the rotational or Lorentz-frame independence of the theory, which is only recovered in the continuum limit. The Baxter 8-vertex model may be regarded as a particular discretization of a self-interacting massive Dirac fermion field theory in two dimensions (the massive Thirring model). Here it is shown that, in the 8-vertex/massive Thirring model, the Lorentz-frame independence of the continuum theory remains undisturbed on the lattice. The only effect of the discretization is to compactify the manifold of Lorentz frames. The relationship between this lattice Lorentz symmetry and the Yang-Baxter relations is discussed.