The delta symbol developed by Duke-Friedlander-Iwaniec and
Heath-Brown has played an important role in studying rational points on
hypersurfaces of low degrees. We present a two dimensional delta symbol
and apply it to establish a quantitative Hasse principle for a smooth
intersection of two quadratic forms defined over Q in at least ten
variables. The goal of these delta symbols is to carry out a (double)
Kloosterman refinement of the circle method. This is based on a joint
work with Simon Rydin Myerson and Pankaj Vishe.