An extended η-regularisation formalism unifies dimensional, denominator, and Schwinger-proper-time regularisation as solutions of gauge consistency conditions, and reproduces the chiral anomaly when implemented with the trace kept inside the integral.
Dimensional regularization vs methods in fixed dimension with and without $\gamma_5$
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abstract
We study the Lorentz and Dirac algebra, including antisymmetric $\epsilon$ tensors and the $\gamma_5$ matrix, in implicit gauge-invariant regularization/renormalization methods defined in fixed integer dimensions. They include constrained differential, implicit and four-dimensional renormalization. We find that these fixed-dimension methods face the same difficulties as the different versions of dimensional regularization. We propose a consistent procedure in these methods, similar to the consistent version of regularization by dimensional reduction.
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Gauge invariance and generalised $\eta$ regularisation
An extended η-regularisation formalism unifies dimensional, denominator, and Schwinger-proper-time regularisation as solutions of gauge consistency conditions, and reproduces the chiral anomaly when implemented with the trace kept inside the integral.