A new treatment of the fermion doubling problem

The problem of fermion doubling occurs in numerical formulations of the Dir ac equation on lattices when the operators of the first derivative are repl aced by difference expressions. The discretization of these operators usual ly leads to unphysical eigensolutions with two different wavenumbers for a single energy. Introducing an unitary transformation U = (1 - iP)/root 2 wh ere P is the spatial parity operator, we obtain a new Dirac equation which can be discretized without the problem of fermion doubling. The example of a free Dirac operator in one dimension is compared with the traditional met hods. (C) 1999 Elsevier Science B.V.