We study the Lorentz and Dirac algebra, including the antisymmetric e tensor
and the y
5 matrix, in implicit gauge-invariant regularization/renormalization methods
de ned in xed integer dimensions. They include constrained differential, implicit and
four-dimensional renormalization. We nd that these xed-dimension methods face the
same di culties 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.The work of A.M.B. and M.P.V. has been supported by the Spanish MINECO project
FPA2016-78220-C3-1-P (Fondos FEDER) and the Junta de Andalucía grant FQM101. The
work of M.P.V. has also been supported by the European Commission, through the contract
PITN-GA-2012-316704 (HIGGSTOOLS). A.L.C. acknowledges nancial support from
CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior), Brazil, as well
as networking support by the COST Action CA16201
