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.
Wodzicki residue and anomalies of current algebras
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The commutator anomalies (Schwinger terms) of current algebras in $3+1$ dimensions are computed in terms of the Wodzicki residue of pseudodifferential operators; the result can be written as a (twisted) Radul 2-cocycle for the Lie algebra of PSDO's. The construction of the (second quantized) current algebra is closely related to a geometric renormalization of the interaction Hamiltonian $H_I=j_{\mu} A^{\mu}$ in gauge theory.
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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.