On the consistency of the regularization of gauge theories by high covariant derivatives

Asorey, Manuel; Falceto, Fernando

doi:10.1103/PhysRevD.54.5290

On the consistency of the regularization of gauge theories by high covariant derivatives

Manuel Asorey
(
- Zaragoza U.
)
,
Fernando Falceto
(
- Zaragoza U.
)

Jan, 1995

25 pages

Published in:

Phys.Rev.D 54 (1996) 5290-5301

e-Print:

hep-th/9502025 [hep-th]

DOI:

10.1103/PhysRevD.54.5290

Report number:

DFTUZ-95-3

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Abstract: (DESY)

We show that regularization of gauge theories by higher covariant derivatives and gauge invariant Pauli-Villars regulators is a consistent method if the Pauli-Villars vector fields are considered in a covariant

\alpha

--gauge with

\alpha\neq 0

. The limit

\alpha\rightarrow 0

in the regulating Pauli-Villars fields is pathological and the original Slavnov proposal in covariant Landau gauge is not correct because of the appearance of massless modes in the regulators which do not decouple when the ultraviolet regulator is removed. In such a case the method does not correspond to the regularization of a pure gauge theory but that of a gauge theory in interaction with massless ghost fields. This explains the problems pointed out by Martin and Ruiz in covariant Landau gauge. However, a minor modification of Slavnov method provides a consistent regularization even for such a case. The regularization that we introduce also solves the problem of overlapping divergences in a way similar to geometric regularization and yields the standard values of the

\beta

and

\gamma

functions of the renormalization group equations.

12.38.Bx
11.15.Bt
gauge field theory: SU(N)
ghost
regularization: Pauli-Villars
regularization: derivative
regularization: geometrical
perturbation theory: higher-order
invariance: Lorentz
renormalization group

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