Background field method as a canonical transformation

Binosi, Daniele; Quadri, Andrea

doi:10.1103/physrevd.85.121702

Cited by 40 publications

(68 citation statements)

References 27 publications

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“…In a similar vein, lattice simulations carried out in the BFM [72,73] may prove instrumental for verifying explicitly some of the formal relations employed throughout this work.…”

Section: Discussionmentioning

confidence: 88%

Gluon mass generation in the massless bound-state formalism

Ibañez

Papavassiliou

2013

Phys. Rev. D

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We present a detailed, all-order study of gluon mass generation within the massless boundstate formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound-states with vanishing mass, which give rise to effective vertices containing massless poles; these latter vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. This particular approach has the conceptual advantage of relating the gluon mass directly to quantities that are intrinsic to the bound-state formation itself, such as the "transition amplitude" and the corresponding "boundstate wave-function". As a result, the dynamical evolution of the gluon mass is largely determined by a Bethe-Salpeter equation that controls the dynamics of the relevant wave-function, rather than the Schwinger-Dyson equation of the gluon propagator, as happens in the standard treatment.The precise structure and field-theoretic properties of the transition amplitude are scrutinized in a variety of independent ways. In particular, a parallel study within the linear covariant (Landau) gauge and the background-field method reveals that a powerful identity, known to be valid at the level of conventional Green's functions, relates also the background and quantum transition amplitudes. Despite the differences in the ingredients and terminology employed, the massless bound-state formalism is absolutely equivalent to the standard approach based on Schwinger-Dyson equations. In fact, a set of powerful relations allow one to demonstrate the exact coincidence of the integral equations governing the momentum evolution of the gluon mass in both frameworks.

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“…In a similar vein, lattice simulations carried out in the BFM [72,73] may prove instrumental for verifying explicitly some of the formal relations employed throughout this work.…”

Section: Discussionmentioning

confidence: 88%

Gluon mass generation in the massless bound-state formalism

Ibañez

Papavassiliou

2013

Phys. Rev. D

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“…As a consequence, the solution cannot be written by simple exponentiation of the BV bracket w.r.t. δΓ δΩ , but requires the introduction of a Lie series of a suitable functional differential operator [27].…”

Section: Background Effective Actionmentioning

confidence: 99%

“…Eventually it has been recognized in a series of papers [25][26][27] that the full dependence on the background field, fixed by the extended ST identity, is induced through a canonical transformation with respect to (w.r.t.) the Batalin-Vilkovisky (BV) bracket of the theory.…”

Section: Introductionmentioning

confidence: 99%

“…Since the latter is in general background-dependent, one cannot obtain the finite form of the canonical transformation by simple exponentiation; rather, one needs to resort to the Lie series of an appropriate functional differential operator. The derivation proceeds in close analogy with the case of parameter-dependent canonical transformations in classical mechanics [27].…”

Section: Introductionmentioning

confidence: 99%

“…This leads to some interesting combinatorial relations of a novel type between one-particle irreducible (1-PI) graphs involving external background sources, whose origin can be ultimately traced back to the canonical transformation of [27], which dictates the dependence of Γ on the backgrounds.…”

Section: Introductionmentioning

confidence: 99%

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Anti-BRST symmetry and background field method

Binosi¹,

Quadri²

2013

Phys. Rev. D

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We show that the requirement that a SU(N) Yang-Mills action (gauge fixed in a linear covariant gauge) is invariant under both the Becchi-Rouet-Stora-Tyutin (BRST) symmetry as well as the corresponding antiBRST symmetry, automatically implies that the theory is quantized in the (linear covariant) background field method (BFM) gauge. Thus, the BFM and its associated background Ward identity naturally emerge from antiBRST invariance of the theory and need not be introduced as an ad hoc gauge fixing procedure. Treating ghosts and antighosts on an equal footing, as required by a BRST-antiBRST invariant formulation of the theory, gives also rise to a local antighost equation that together with the local ghost equation completely resolve the algebraic structure of the ghost sector for any value of the gauge fixing parameter. We finally prove that the background fields are stationary points of the background effective action obtained when the quantum fields are integrated out.

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Off-shell renormalization in the presence of dimension 6 derivative operators. Part III. Operator mixing and β functions

Binosi

Quadri

2020

J. High Energ. Phys.

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We evaluate the one-loop β functions of all dimension 6 parity-preserving operators in the Abelian Higgs-Kibble model. No on-shell restrictions are imposed; and the (generalized) non-polynomial field redefinitions arising at one-loop order are fully taken into account. The operator mixing matrix is also computed, and its cancellation patterns explained as a consequence of the functional identities of the theory and powercounting conditions.

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Background field method as a canonical transformation

Cited by 40 publications

References 27 publications

Gluon mass generation in the massless bound-state formalism

Gluon mass generation in the massless bound-state formalism

Anti-BRST symmetry and background field method

Off-shell renormalization in the presence of dimension 6 derivative operators. Part III. Operator mixing and β functions

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