Integral formula for the characteristic Cauchy problem on a curved background

We give a local integral formula, valid on general curved spacetimes, for the characteristic Cauchy problem for the Dirac equation with arbitrary spin. The derivation of the formula is based on the work of Friedlander (1975) [6] for the wave equation. A parametrix for the square of the Dirac operator, which is a spinor wave equation, is built using Friedlander's construction. Deriving the representation formula obtained in function of the characteristic data for this particular wave equation gives an integral formula for the Goursat problem. The results obtained by Penrose (1963) in the flat case in [21] are recovered directly. (C) 2010 Elsevier Masson SAS. All rights reserved.