Noether Theorems and Discrete Variational Integrators in Field Theory

The discrete analogue of the Noether-type identities in eld theory is investigated by means of the di erence discrete variational principle in which the di erence is regarded as an entire geometric object. The discrete counterparts of the Noether theorems are obtained. It is proved that there exists the discrete version of the Noether conservation law in eld theory. The discretization for the nonlinear Schrodinger equation is presented to illustrate the results.