Algebra for a BRST Quantization of Metric-Affine Gravity

Mielke, Eckehard W.; Maggiolo, Alí A. Rincón

doi:10.1023/a:1022939019252

Cited by 9 publications

(8 citation statements)

References 34 publications

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“…Thus it seems that there is still room for a quantization program based on Yang's theory of gravity, departing, in a gauge covariant approach, from the nilpotency of the corresponding BRST charges [42] and the operator version of the constraint (13), or even from superconnections [43]. I was very please to get your letter of July 5, which reached me here a few days ago.…”

Section: Discussionmentioning

confidence: 99%

Duality in Yang’s theory of gravity

Mielke

Maggiolo

2005

Gen Relativ Gravit

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The historical route and the current status of a curvature-squared model of gravity, in the affine form proposed by Yang, is briefly reviewed. Due to its inherent scale invariance, it enjoys some advantage for quantization, similarly as internal Yang-Mills fields. However, the exact vacuum solutions with double duality properties exhibit a 'vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only the Einstein equations with induced cosmological constant emerge for the classical background, even when coupled to matter sources.

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Section: Discussionmentioning

confidence: 99%

Duality in Yang’s theory of gravity

Mielke

Maggiolo

2005

Gen Relativ Gravit

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“…Consequently, there is still a valid avenue to a consistent quantization based on a topological version of selfdual SKY gravity, departing, in a gauge covariant approach, from a d-exact topological term. Due to the nilpotency of the corresponding BRST charges [45], the s-exact term can easily account for the necessary gauge constraints such as (15) implying Einsteinian gravity for the classical 'background'. This, to some extent, provides an answer to the issue already raised 1963 by Feynman [21], whether Einstein's GR, in view of its force-free geometrical concepts, needs to be quantized at all or if curved spacetime can be left as an arena for quantized (topological) fields to play out.…”

Section: Einstein Equation With Induced Cosmological Constant and Aximentioning

confidence: 99%

“…Refs. [45,63], Ψ := i 4 Ψ αβ j σ αβ dx j the topological ghost one-form and Φ := i 4 Φ αβ σ αβ the corresponding ghost of the topological ghost. All are Lie algebra-valued due to the appearance of the generator σ αβ of the linear (or Lorentz) group.…”

Section: Appendix B: Brst Transformationsmentioning

confidence: 99%

Einsteinian gravity from a topological action

Mielke

2008

Gen Relativ Gravit

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Abstract.The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background.However, exact vacuum solutions with double duality properties exhibit a 'vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only Einstein's equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of 'dark energy' as well as 'dark matter' modeled by a torsion induced quintaxion.

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Section: Einstein Equation With Induced Cosmological Constant and Aximentioning

confidence: 99%

Publisher’s Note: Einsteinian gravity from BRST quantization of a topological action [Phys. Rev. D77, 084020 (2008)]

Mielke¹

2008

Phys. Rev. D

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INTRODUCTIONOn the macroscopical level, Einstein's general relativity has passed every test "with flying colors", see Will [67] for a recent review. However, Einstein's theory sofar has resisted any attempt of quantization, e.g. it is known to be perturbatively nonrenormalizable, partially due to its dimensional coupling constant 2 . String theory or brane scenarios with extra dimensions have been proposed as a rescue, some of which are implying, however, deviations of standard gravity in the sub-millimeter range. Recent torsion balance experiments [28] have probed the inverse square law and found no deviation even below the hypothetical dark energy (DE) scale of λ DE = (hc/ρ DE ) 1/4 ≃ 85 µm. Thus this 'window' of possibly new gravitational physics seems also to be closing.In 1974 Yang proposed an affine gauge theory gravity [70] which, due to its scale invariance, can be regarded as a rather promising fundamental theory of (quantum) gravity in the high-energy limit [25], without invoking extra dimensions or supersymmetry, cf. Ref. [30]. An additional duality constraint on the curvature could be extremely important for the path integral approach to quantum gravity. Then instanton type configurations [22] near the classical ones, i.e. Einstein spaces, are more probable then the 'spurious' Thomson spaces, as one would expect naively. For the modified duality with a breaking of scale invariance, the transition amplitude peaks at classical Einstein spaces only. Alternatively, in a four-dimensional Yang-Mills theory gauging the de Sitter group [37,54], scale invariance gets spontaneously broken by a pseudo-Goldstone type 'radius vector' [62], odd under CP, in order to recover the Hilbert-Einstein action plus the Euler term.From the work of Stelle [59] we know that the curvature squared gravity in Riemannian spacetime is perturbatively renormalizable but unfortunately plagued with physical ghost, i.e. negative residues in the graviton propagator [36]. This finding has diminished 1 E-mail: ekke@xanum.uam.mx 2 It has to be kept in mind that Newton's gravitational constant G is one of the less precise known constants of physics. In order to improve this situation, there are plans [1] to measure the gravitational attraction of two bodies in a spaceship (Project SEE), where the larger body will function as a shepherd for the movement of the test mass, similarly as in the rings of Saturn. Amongst others, an accuracy of 3.3 × 10 −7 in the determination of G should be feasible. the initial interest [19,20] in such models.Much more promising and elegant is to start from a purely topological classical action, proportional to the gravitational Pointrjagin (or Euler) invariant and then quantize this model by nilpotent Becchi-Rouet-Stora-Tyutin (BRST) transformations generated by s. Such a topological action is not only completely metric-free, but moreover conformally invariant [69,34] and can provide a consistent Topological Quantum Field Theory (TQFT) as shown by Witten [68,9]. Lateron, it was realized by Baulieu and Singer [6]...

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Algebra for a BRST Quantization of Metric-Affine Gravity

Cited by 9 publications

References 34 publications

Duality in Yang’s theory of gravity

Duality in Yang’s theory of gravity

Einsteinian gravity from a topological action

Publisher’s Note: Einsteinian gravity from BRST quantization of a topological action [Phys. Rev. D77, 084020 (2008)]

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