  A scheme is presented to decompose the exponential of a two-body operator in
a discrete sum over exponentials of one-body operators. This discrete
decomposition can be used instead of the Hubbard-Stratonovich transformation in
auxiliary-field quantum Monte-Carlo methods. As an illustration, the
decomposition is applied to the Hubbard model, where it is equivalent to the
discrete Hubbard-Stratonovich transformation introduced by Hirsch, and to the
nuclear pairing Hamiltonian.
