  We exhibit central simple algebras over the function field of a diagonal
quartic surface over the complex numbers that represent the 2-torsion part of
its Brauer group. We investigate whether the 2-primary part of the Brauer group
of a diagonal quartic surface over a number field is algebraic and give
sufficient conditions for this to be the case. In the last section we give an
obstruction to weak approximation due to a transendental class on a specific
diagonal quartic surface, an obstruction which cannot be explained by the
algebraic Brauer group which in this case is just the constant algebras.
