Proof of perturbative gauge invariance for tree diagrams to all orders

Dütsch, Michael

doi:10.1002/andp.200510145

Cited by 9 publications

(27 citation statements)

References 34 publications

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“…The theorem in [45] of course fits with our construction. The previous analysis allows one next 2 Some of the authors of that reality check openly suspected SSB as a formal recipe without physical meaning; others were swayed by the remarkable "success rate" of the Higgs mechanism; some apparently remained agnostic.…”

Section: Outline Of the Sequelsupporting

confidence: 61%

“…The first method is constructive. The second, stemming from a theorem by one of us in [45], is useful rather to verify CGI. Section 3 summarizes the first results of the theory.…”

Section: Outline Of the Sequelmentioning

confidence: 99%

“…-In the opposite direction, i.e. postulating the underlying gauge symmetry, we expect that models built by SSB be classically BRST invariant, and hence satisfy CGI at tree level to all orders [45].…”

Section: The Relation Between Cgi and Ssbmentioning

confidence: 99%

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Quantum gauge models without (classical) Higgs mechanism

Dütsch¹,

Gracia‐Bondía

Scheck

et al. 2010

Eur. Phys. J. C

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We examine the status of massive gauge theories, such as those usually obtained by spontaneous symmetry breakdown, from the viewpoint of causal (EpsteinGlaser) renormalization. The BRST formulation of gauge invariance in this framework, starting from canonical quantization of massive (as well as massless) vector bosons as fundamental entities, and proceeding perturbatively, allows one to rederive the reductive group symmetry of interactions, the need for scalar fields in gauge theory, and the covariant derivative. Thus the presence of higgs particles is understood without recourse to a Higgs(-Englert-BroutGuralnik-Hagen-Kibble) mechanism. Along the way, we dispel doubts about the compatibility of causal gauge invariance with grand unified theories."Sire, je n'avais pas besoin de cette hypothèse-là" -Pierre Simon de Laplace

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Section: Outline Of the Sequelsupporting

confidence: 61%

“…The first method is constructive. The second, stemming from a theorem by one of us in [45], is useful rather to verify CGI. Section 3 summarizes the first results of the theory.…”

Section: Outline Of the Sequelmentioning

confidence: 99%

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Quantum gauge models without (classical) Higgs mechanism

Dütsch¹,

Gracia‐Bondía

Scheck

et al. 2010

Eur. Phys. J. C

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“…(The corresponding renormalization map D (3.22) is given in [27].) Our definitions of T c tree (4.8) and Ttree (4.10) do not contain this 1/2 g µν δ-term, in agreement with the definition of R cl (2.17).…”

Section: Diagrammatics and Definition Of The 1-particle-irreducible Psupporting

confidence: 58%

“…The violation of the conservation of j(g) is expressed in terms of the Q-vertex [13,2,1]: in Sects. 3 and 4 of [27] it is shown that for the considered models there exists a Q-vertex L (1) (g) such that…”

Section: Assumption: Localized Off-shell Version Of Noether's Theoremmentioning

confidence: 99%

Removal of Violations of the Master Ward Identity in Perturbative QFT

2008

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We study the appearance of anomalies of the Master Ward Identity, which is a universal renormalization condition in perturbative QFT. The main insight of the present paper is that any violation of the Master Ward Identity can be expressed as a local interacting field; this is a version of the well-known Quantum Action Principle of Lowenstein and Lam. Proceeding in a proper field formalism by induction on the order in , this knowledge about the structure of possible anomalies as well as techniques of algebraic renormalization are used to remove possible anomalies by finite renormalizations. As an example the method is applied to prove the Ward identities of the O(N ) scalar field model.

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Notes on “Quantum Gravity” and Noncommutative Geometry

Gracia‐Bondía

2010

Lecture Notes in Physics

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I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide against just selling my mathematical wares, and for a survey, necessarily very selective, but taking a global phenomenological approach to its subject matter. After all, noncommutative geometry does not purport yet to solve the riddle of quantum gravity; it is more of an insurance policy against the probable failure of the other approaches. The plan is as follows: the introduction invites students to the fruitful doubts and conundrums besetting the application of even classical gravity. Next, the first experiments detecting quantum gravitational states inoculate us a healthy dose of scepticism on some of the current ideologies. In Section 3 we look at the action for general relativity as a consequence of gauge theory for quantum tensor fields. Section 4 briefly deals with the unimodular variants. Section 5 arrives at noncommutative geometry. I am convinced that, if this is to play a role in quantum gravity, commutative and noncommutative manifolds must be treated on the same footing; which justifies the place granted to the reconstruction theorem. Together with Section 3, this part constitutes the main body of the notes. Only very summarily at the end of this section we point to some approaches to gravity within the noncommutative realm. The last section delivers a last dose of scepticism. My efforts will have been rewarded if someone from the young generation learns to mistrust current mindsets.

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Proof of perturbative gauge invariance for tree diagrams to all orders

Abstract: It is proved that classical BRS-invariance of the Lagrangian implies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Largrangian of gravity.

Cited by 9 publications

References 34 publications

Quantum gauge models without (classical) Higgs mechanism

Quantum gauge models without (classical) Higgs mechanism

Removal of Violations of the Master Ward Identity in Perturbative QFT

Notes on “Quantum Gravity” and Noncommutative Geometry

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