Finite Size Corrections for One Dimensional Interacting Fermions

Using the method based on the Euler-Maclaurin formula, we calculate the finitesize correction to the energy of the ground state and the excited state for the delta interacting fermion gas in the periodic boundary condition with N - 1 of the N fermions having the same spin and one having the opposite spin. In the thermodynamic limit, we obtain the conformal anomaly, operator dimension and the correlation functions.