Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part I

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.