Higher order calculation in thermo field theory

We perform higher order calculations at finite temperature by the use of thermo field theory. It is shown that the terms involving deltasup(N)(k2-m2) (N>=2) characteristic of the real time formalism become well-defined in thermo field theory. The taming of the singularity is concisely understood by the use of a derivative formula. Further we find a great simplification in the calculation of the singular diagrams. The calculation is partially carried out also in the Imaginary Time Formalism for the sake of comparison. The disposition of the imaginary parts in thermo field theory is also discussed. (orig.)