Equivalence theorem and Faddeev-Popov ghosts

Bergère, M. C.; Lam, Yuk‐Ming P.

doi:10.1103/physrevd.13.3247

Cited by 69 publications

(85 citation statements)

References 22 publications

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“…Nevertheless, the so-called equivalence theorem, which formalizes this independence, has been proved rigorously [8], using the renormalized quantum action principles [9,10]. We shall extend this proof to HQEFT below.…”

Section: Introductionmentioning

confidence: 99%

“…Having defined the S-matrix for heavy quark states, the proof that the Smatrix is unchanged by reparametrizations, i.e., that the S-matrix elements calculated from the original HQEFT are the same as those calculated with the new Lagrangian obtained by the change of variables (31), proceeds exactly as in ordinary quantum field theory [8]. The additional terms in the Green's functions on the right-hand side of (32) contribute in such a way that the residue of the pole at v · k + k 2 /2m = 0 (which appears as a series of multiple poles in the effective theory) is multiplied by some function of k identical for all Green's functions of the heavy quark.…”

Section: The Equivalence Theorem For the S-matrixmentioning

confidence: 99%

See 1 more Smart Citation

Renormalization of heavy quark effective field theory: Quantum action principles and equations of motion

Kilian

Ohl

1994

Phys. Rev. D

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Section: Introductionmentioning

confidence: 99%

Section: The Equivalence Theorem For the S-matrixmentioning

confidence: 99%

Renormalization of heavy quark effective field theory: Quantum action principles and equations of motion

Kilian

Ohl

1994

Phys. Rev. D

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“…(3) a set of external sources will be necessary as for instance a term involving the new field ϕ and the Faddeev-Popov ghosts which will be introduced in order to take into account the determinant. It has been noticed in [13] that a simpler formulation of the ET can be given if one neglects the Jacobian of the transformation. In this case the ET takes the form…”

Section: Introductionmentioning

confidence: 99%

“…Moreover all known proofs of the ET are based on the validity of the Quantum Action Principle (QAP), which is valid for power-counting renormalizable theories. In the pioneer papers it is assumed either that there is only one derivative for each field in the vertex (BPHZ framework) [12,13] or that the Feynman propagators are standard ((p 2 − m 2 ) −1 for bosons and (/ p − m) −1 for fermions) and there are no derivative vertices (dimensional regularization) [14]. In [15] the proof of QAP is extended to the massless case for a power-counting renormalizable theory.…”

Section: Introductionmentioning

confidence: 99%

An Approach to the Equivalence Theorem by the Slavnov-Taylor Identities

Ferrari¹,

Picariello²,

Quadri³

2002

J. High Energy Phys.

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We discuss the Equivalence Theorem (ET) in the BRST formalism. In particular the SlavnovTaylor (ST) identities, derived at the formal level in the path-integral approach, are considered at the quantum level and are shown to be always anomaly free.Some discussion is devoted to the transformation of the fields; in fact the existence of a local inverse (at least as a formal power expansion) suggests a formulation of the ET, which allows a nilpotent BRST symmetry. This strategy cannot be implemented at the quantum level if the inverse is non-local. In this case we propose an alternative formulation of the ET, where, by using FaddeevPopov fields, this difficulty is circumvented. In fact this approach allows the loop expansion both in the original and in the transformed theory. In this case the algebraic formulation of the problem can be simplified by introducing some auxiliary fields. The auxiliary fields can be eliminated by using the method of Batalin-Vilkovisky.We study the quantum deformation of the associated ST identity and show that a selected set of Green functions, which in some cases can be identified with the physical observables of the model, does not depend on the choice of the transformation of the fields. The computation of the cohomology for the classical linearized ST operator is performed by purely algebraic methods. We do not rely on power-counting arguments.In general the transformation of the fields yields a non-renormalizable theory. When the equivalence is established between a renormalizable and a non-renormalizable theory, the ET provides a way to give a meaning to the last one by using the resulting ST identity. In this case the Quantum Action Principle cannot be of any help in the discussion of the ET. We assume and discuss the validity of a Quasi Classical Action Principle, which turns out to be sufficient for the present work.As an example we study the renormalizability and unitarity of massive QED in Proca's gauge by starting from a linear Lorentz-covariant gauge.

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“…There has been some important progress in the use of field redefinition and its relation with the renormalization procedure [13], [14] and with the algebraic structure of the theory [15]- [24]. However, to my knowledge, no one has directly faced the task of taming the difficulties urging from the arbitrariness of the counterterms in conventional renormalization procedure.…”

Section: On the Conventional Approachmentioning

confidence: 99%