Quantum dynamics of Lagrange multipliers

Álvarez, Enrique Alarcón; Anero, Jesús; Martı́n, C.P.; Velasco-Aja, Eduardo

doi:10.1103/physrevd.108.026013

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…As also shown in Ref. [17] the problem goes away if the so-called exponential splitting [18] is used. We think that it is quite a drawback to have a formalism where the classic linear splitting -which is standardly used in General Relativity -cannot be employed.…”

Section: Introductionmentioning

confidence: 70%

“…It has been shown recently -see Ref. [17] -that the unimodularity condition cannot be implemented in the path integral by using a Lagrange multiplier unless the unimodularity condition be equivalent to imposing a linear constraint on the graviton field. This fact precludes the use of the classic linear splitting of the gravity field into background metric and graviton field if the unimodularity condition is to be enforced by using a Lagrange multiplier.…”

Section: Introductionmentioning

confidence: 99%

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Quantization of Weyl invariant unimodular gravity with antisymmetric ghost fields

García-López,

Martin

2024

Eur. Phys. J. C

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The enforcement of the unimodularity condition in a gravity theory by means of a Lagrange multiplier leads, in general, to inconsistencies upon quantization. This is so, in particular, when the classic linear splitting of the metric between the background and quantum fields is used. To avoid the need of introducing such a Lagrange multiplier while using the classic linear splitting, we carry out the quantization of unimodular gravity with extra Weyl symmetry by using Becchi–Rouet–Stora–Tyutin (BRST) techniques. Here, two gauge symmetries are to be gauge-fixed: transverse diffeomorphisms and Weyl transformations. We perform the gauge-fixing of the transverse diffeomorphism invariance by using BRST transformations that involve antisymmetric ghost fields. We show that these BRST transformations are compatible with the BRST transformations needed to gauge-fix the Weyl symmetry, so that they can be combined in a set of transformations generated by a single BRST operator. Newton’s law of gravitation is derived within the BRST formalism we put forward as well as the Slavnov–Taylor equation.

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Section: Introductionmentioning

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Quantization of Weyl invariant unimodular gravity with antisymmetric ghost fields

García-López,

Martin

2024

Eur. Phys. J. C

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The one-loop unimodular graviton propagator in any dimension

Anero

Martı́n

Velasco-Aja

2023

J. High Energ. Phys.

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For unimodular gravity, we work out, by using dimensional regularization, the complete one-loop correction to the graviton propagator in any space-time dimension. The computation is carried out within the framework where unimodular gravity has Weyl invariance in addition to the transverse diffeomorphism gauge symmetry. Thus, no Lagrange multiplier is introduced to enforce the unimodularity condition. The quantization of the theory is carried out by using the BRST framework and there considering a large continuous family of gauge-fixing terms. The BRST formalism is developed in such a way that the set of ghost, anti-ghost and auxiliary fields and their BRST changes do not depend on the space-time dimension, as befits dimensional regularization. As an application of our general result, and at D = 4, we obtain the renormalized one-loop graviton propagator in the dimensional regularization minimal subtraction scheme. We do so by considering two simplifying gauge-fixing choices.

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Field redefinition invariant Lagrange multiplier formalism with gauge symmetries

McKeon,

Brandt,

Martins-Filho

2024

Eur. Phys. J. C

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It has been shown that by using a Lagrange multiplier field to ensure that the classical equations of motion are satisfied, radiative effects beyond one-loop order are eliminated. It has also been shown that through the contribution of some additional ghost fields, the effective action becomes form invariant under a redefinition of field variables, and furthermore, the usual one-loop results coincide with the quantum corrections obtained from this effective action. In this paper, we consider the consequences of a gauge invariance being present in the classical action. The resulting gauge transformations for the Lagrange multiplier field as well as for the additional ghost fields are found. These gauge transformations result in a set of Faddeev–Popov ghost fields arising in the effective action. If the gauge algebra is closed, we find the Becci–Rouet–Stora–Tyutin (BRST) transformations that leave the effective action invariant.

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Quantum dynamics of Lagrange multipliers

Cited by 3 publications

References 13 publications

Quantization of Weyl invariant unimodular gravity with antisymmetric ghost fields

Quantization of Weyl invariant unimodular gravity with antisymmetric ghost fields

The one-loop unimodular graviton propagator in any dimension

Field redefinition invariant Lagrange multiplier formalism with gauge symmetries

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