  The theory of affine processes on the space of positive semidefinite d x d
matrices has been established in a joint work with Cuchiero, Filipovi\'c and
Teichmann (2011). We confirm the conjecture stated therein that in dimension d
greater than 1 this process class does not exhibit jumps of infinite total
variation. This constitutes a geometric phenomenon which is in contrast to the
situation on the positive real line (Kawazu and Watanabe, 1974). As an
application we prove that the exponentially affine property of the Laplace
transform carries over to the Fourier-Laplace transform if the diffusion
coefficient is zero or invertible.
