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Wodzicki residue and anomalies of current algebras

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arxiv hep-th/9404093 v2 pith:QFSSC5LL submitted 1994-04-15 hep-th math.QA

classification hep-thmath.QA
keywords currentalgebraalgebrasanomaliesresiduetermswodzickiclosely
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abstract

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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  1. Gauge Choices, Infrared Pitfalls, and Thermal Effects in Effective Potentials

    hep-th 2025-07 conditional novelty 5.0 of 10

    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.

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