  The string-inspired technique is used for the calculation of vacuum
polarisation tensors in constant electromagnetic fields. In the first part of
this series, we give a detailed exposition of the method for the case of the
QED one-loop N-photon amplitude in a general constant electromagnetic
background field. The two-point cases are calculated explicitly, leading to
compact representations for the constant field vacuum polarisation tensors for
both scalar and spinor QED.
