Two-Loop Finite Temperature Effective Potential. I: Real Scalar Theory with Cubic Term

Abstract
The two-loop finite temperature effective potential of a single real scalar inculuding cubic term is calculated by the use of Thermo Field Dynamics. The calculation is carried out by both the tadpole and vacuum graph techniques, and they are found to agree. It is explicitly shown that the temperature-dependent divergent terms cancel each other and the product of delta functions causes no difficulty, the latter fact being compactly summarized as mass derivative formula.

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