It is suggested that the fermion determinant for a vector-like gauge theory with strictly massless quarks can be represented on the lattice as $\det{{1+V}\over 2}$, where $V=X(X^\dagger X)^{-1/2}$ and $X$ is the Wilson-Dirac lattice operator with a negative mass term. There is no undesired doubling and no need for any fine tuning. Several other appealing features of the formula are pointed out.Comment: 7 pages, plain TeX; references correcte

Path integration over Euclidean chiral fermions is replaced by the quantum mechanics of an auxiliary system of non{interacting fermions. Our construction avoids the no{go theorem and faithfully maintains all the known important features of chiral fermions, including the violation of some perturbative conservation laws by gauge eld con gurations of non{trivial topology.

A practical implementation of the Overlap-Dirac operator 1+γ 5 ǫ(H) 2 is presented. The implementation exploits the sparseness of H and does not require full storage. A simple application to parity invariant three dimensional SU (2) gauge theory is carried out to establish that zero modes related to topology are exactly reproduced on the lattice.

An expression for the lattice e ective action induced by chiral fermions in any even dimensions in terms of an overlap of two states is shown to have promising properties in two dimensions: The correct abelian anomaly is reproduced and instantons are suppressed.

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