  In string theory, there are various physical situations where the world-sheet
fields have a shifted moding. For instance, this is the case for the twisted
closed string in Z_N orbifold or for the charged open string in a constant
electro-magnetic field. Because of this feature, it is quite challenging to
give explicit formulae describing the string interaction, even for the bosonic
case. In this note, we focus on the case of the charged open bosonic string and
construct the 1-loop tadpole which is an object generating all 1-point
functions from the annulus in the presence of an external field. In the
operator formalism, this represents one of the basic building blocks for the
construction of a general loop amplitude.
