Including a multiplicative anomaly or using the Heat Kernel method makes the one-loop effective potential in the Fermi gauge independent of the gauge parameter and improves its infrared behaviour, also at finite temperature.
Complete determination of the singularity structure of zeta functions
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abstract
Series of extended Epstein type provide examples of non-trivial zeta functions with important physical applications. The regular part of their analytic continuation is seen to be a convergent or an asymptotic series. Their singularity structure is completely determined in terms of the Wodzicki residue in its generalized form, which is proven to yield the residua of all the poles of the zeta function, and not just that of the rightmost pole (obtainable from the Dixmier trace). The calculation is a very down-to-earth application of these powerful functional analytical methods in physics.
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Gauge Choices, Infrared Pitfalls, and Thermal Effects in Effective Potentials
Including a multiplicative anomaly or using the Heat Kernel method makes the one-loop effective potential in the Fermi gauge independent of the gauge parameter and improves its infrared behaviour, also at finite temperature.