Chiral symmetry and O(alpha) improvement in lattice QCD

The dominant cutoff effects in lattice QCD with Wilson quarks are proportional to the lattice spacing a. In particular, the isovector axial current satisfies the PCAC relation only up to such effects. Following a suggestion of Symanzik, they can be cancelled by adding local O(a) correction terms to the action and the axial current. We here address a number of theoretical issues in connection with the O(a) improvement of lattice QCD and then show that chiral symmetry can be used to fix the coefficients multiplying the correction terms.