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We construct an invariant basis for Compton scattering with two virtualphotons (VVCS). The basis tensors are chosen to be gauge invariant andorthogonal to each other. The properties of the corresponding 18 invariantamplitudes are studied in detail. We consider the special case of elastic VVCSwith the virtualities of the initial and final photons equal. The invariantbasis for VVCS in this orthogonal form does not exist in the literatur. Wefurthermore use this VVCS tensor for a calculation of the beam normal spinasymmetry in the forward kinematics. For this, we relate the invariantamplitudes to the helicity amplitudes of the VVCS reaction. The imaginary partsof these latter are related to the inclusive cross section by means of theoptical theorem. We use the phenomenological value of the transverse crosssection $\sigma_T\sim0.1$ mbarn and the Callan-Gross relation which relates thelongitudinal cross section $\sigma_L$ to the transverse one. The result of thecalculation agrees with an existing calculation and predicts the negativevalues of the asymmetry $B_n$ of the order of 4-6 ppm in the energy range from6 to 45 ppm and for very forward angles.Comment: 13 pages, 2 figures, revtex, submitted to Phys. Rev. C; new version:  two figures added, typos correcte

Doubly virtual Compton scattering and the beam normal spin asymmetry