### Citations

29 |
New Perspectives in Canonical Gravity,” Bibliopo ersity dge
- Ashtekar
- 2004
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Citation Context ... is nondegenerate. I think this is one of the central problems for quantum gravity. It has been discussed recently in the context of Ashtekar’s reformulation of GR, which admits gµν = 0 as a solution =-=[11,12,7]-=-. However in GR there seems to be no local dynamical mechanism to favor a nondegenerate metric over the zero metric. The choice seems to be dictated by boundary conditions [13]. What we want instead i... |

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Geometry on Nonlinear Field Theories, World Scientific
- Percacci
- 1986
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Citation Context ...ism In order to understand in what sense a Higgs phenomenon can be said to occur in GR, it will be convenient to use a particular formalism which exhibits invariance under local GL(4) transformations =-=[2,3]-=- (there are also different ways of seeing gravity as a spontaneously broken GL(4) gauge theory [4]). Every theory of gravity can be presented in the GL(4) formalism. We review the relevant aspects her... |

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D 30 305
- Rev
- 1984
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Citation Context ...onvenient to use a particular formalism which exhibits invariance under local GL(4) transformations [2,3] (there are also different ways of seeing gravity as a spontaneously broken GL(4) gauge theory =-=[4]-=-). Every theory of gravity can be presented in the GL(4) formalism. We review the relevant aspects here; a more complete discussion in geometric language has been given in [3]. The GL(4)-invariant for... |

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Topological GL(3)-invariant gravity”, preprint SISSA 97/90/EP
- Floreanini, Percacci
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Citation Context ... the relevant aspects here; a more complete discussion in geometric language has been given in [3]. The GL(4)-invariant formulation of GR has also been studied in Hamiltonian form in a recent trilogy =-=[5,6,7]-=-. In the GL(4) formalism, the independent dynamical variables describing the gravitational field are an IR4-valued one-form θaµ, scalar fields κab in the symmetric tensor representation of GL(4) and, ... |

1 |
of Physics 62
- Isham, Salam, et al.
- 1971
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Citation Context ... just an analogy: since the space of lorentzian metrics in IR4 can be identified with the homogeneous space GL(4)/O(1, 3), the fiber metric κ is literally a GL(4)/O(1, 3)–valued nonlinear sigma model =-=[3,8]-=-. In the GL(4) formalism, the torsion and the nonmetricity of the connection A are defined as follows. The torsion of A with respect to θ is Θµ a ν = ∂µθ a ν − ∂νθaµ + Aµab θbν − Aνab θbµ . (6) The no... |

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in “Fibre bundles: their use
- Percacci
- 1988
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Citation Context ...g), A (N−4) λab = −A(N−4)λba , Hλab = −Kλba and Kλ a bθ b τ = Kτ a bθ b λ. Thus when θ and κ have maximal ranks, the solutions of the equations Θ = 0 and ∆ = 0 depend on 2N(N − 4) arbitrary functions =-=[16]-=-. A consequence of this is that if we were to repeat the analysis of section 3 in the case N > 4, the equations of motion would not determine A completely. For this and other reasons which will become... |

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Why is the metric nondegenerate?”, preprint SISSA 132/90/EP
- Floreanini, Percacci, et al.
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Citation Context ... separate variable, while useful at this stage, may not be necessary in the construction of a realistic model. As a first try, it is natural to consider a model in which κab = ℓ −1ηab from the outset =-=[1,19]-=-. 14 The construction of a realistic grand unified theory will require also the introduction of spinor fields. Here there are various possibilities. If the theory can be consistently quantized with th... |

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Postscript, december 2007 Several developments have taken place in the last few years. There is now a number of papers that discuss a form of “Gravitational Higgs Phenomenon” (GHP) which is different from the one that was introduced here. Some representat
- Phys
- 1957
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Citation Context ...tric, the net effect being a cutoff on momentum integrations at Planck’s mass. In this way the “Higgs picture” may provide an implementation of the old idea that gravity acts as a universal regulator =-=[23]-=-. Critics say that the Higgs mechanism is only an ad hoc construction and should not be taken as a description of nature at the fundamental level. Instead, the explanation of the origin of masses shou... |

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e-Print: arXiv:0708.3184 [hep-th
- Hooft
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Citation Context ...1gµν for µ, ν = 1, 2, 3, 4. The residual 10 gauge group consists of coordinate transformations and localG(N,4) transformations, where G(N,4) denotes the group of matrices of the form Λ = [ 14 a 0 b ] =-=(26)-=- with b ∈ GL(N − 4). If (2′) holds, the N -bein gauge is defined by the condition κab = ℓ−1ηab; in this gauge local GL(N) invariance is broken to local O(1, N − 1) invariance. It is still true that th... |

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e-Print: arXiv:0710.1061 [hep-th
- Kakushadze
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Citation Context ...ric gauge, one can further impose that κab = ℓ −1δab for a, b = 5, . . . , N and κab = 0 for a = 1, 2, 3, 4 and b = 5, . . . , N or vice-versa. So altogether θ = ℓ−1 [ 14 0 ] , κ = ℓ−1 [ g 0 0 1N−4 ] =-=(27)-=- We will call this the extended metric gauge. In this gauge local GL(N) invariance is broken down to local O(N − 4) invariance. If θ and κ have maximal ranks, the internal space at each point x can be... |

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e-Print: arXiv:0801.0827 [hep-th] To clarify the distinction, let me call (for want of a better name) “High Energy GHP” the one discussed in this paper and “Low Energy GHP” the one discussed in the papers mentioned above. The following table highlights th
- Maeno, Oda
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Citation Context ... im θ(x)⊕ζx, where im θ(x) denotes the image of θ and ζ is the orthogonal complement. Accordingly, the gauge field Aλ a b can be decomposed naturally in four parts: Aλ = [ A (4) λ Hλ Kλ A (N−4) λ ] . =-=(28)-=- In the extended metric gauge, the components A (4) λ can be identified with the components of the induced connection on spacetime (4′), the components A(N−4)λ represent a purely internalGL(N−4) Yang-... |

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Annals Phys. 321 708-743 (2006), e-Print: gr-qc/0502005 An interesting discussion of gravitational Nambu-Goldstone fields in the context of Lorentz– violating theories, and the associated Higgs phenomenon, can be
- Leclerc
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Citation Context ...ut for the purpose of illustration it will be sufficient to consider the following terms: S̄m(θ, κ, A; θ̄, κ̄) = 1 2 ∫ d4x √ | det ḡ| [A1ℓ ḡµρḡνσκ̄ab∇̄µθaν∇̄ρθbσ +B1ℓ −2ḡµν κ̄acκ̄bd∇µκab∇νκcd ] . =-=(30)-=- In the potential U given in equation (22), ℓ−1θ̄−1aµ has to be replaced by ℓ2θ̄aµ. We then observe that with the background fields given below, this potential does not depend on the components θaµ wi... |

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The unification scheme based on the HEGHP has been recently reexamined in some more detail
- Kostelecky, D71
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Citation Context ...lementary approach of trying to reconcile the quantum theory with the nonlinearity implicit in the constraints. 8 One could consider also other potential terms, for example the ones given in equation =-=(31)-=-, but these would not lead to any qualitatively new feature. Powers of ℓ have been inserted to compensate for the dimension of the background fields (see the Appendix; these factors disappear when we ... |

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e-Print: arXiv:0706.3307 [hep-th
- Nesti, Percacci
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Citation Context ... the action is expanded to second order around this ground state, S̄m gives rise to a term of the type 1 2 ℓ−2 ∫ d4x [ A1η µνAµ a cAν b d ηabP c fP d gη fg +B1η µνηacηbd(Aµab + Aµba)(Aνcd + Aνdc) ] . =-=(32)-=- In order to diagonalize the mass matrix we define the combinations A (4,±) λab = 1 2 (A (4) λab ± A(4)λba) , (33a) A (N−4,±) λab = 1 2 (A (N−4) λab ±A(N−4)λba ) , (33b) H (±) λab = 1√ 2 (√ 1∓ A1√ A21... |

1 | e-Print: arXiv:0706.4481 [hep-th] The “exceptionally simple” E8 unification of - Alexander |

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e-Print: arXiv:0711.0770 [hep-th] belongs to the same class of models, where the gravitational and Yang–Mills connections are considered as parts of the connection of a larger group. Lisi tries to go further by putting also all other fields in the same re
- Lisi
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Citation Context ... [ (A1+4B1)A (4,+) µab A (4,+) ν ab+A1A (4,−) µab A (4,−) ν ab+4B1A (N−4,+) µab A (N−4,+) ν ab + 1 2 ( A1+2B1+ √ A21+4B 2 1 ) H (+) µabH (+) ν ab+ 1 2 ( A1+2B1− √ A21+4B 2 1 ) H (−) µabH (−) ν ab ] . =-=(34)-=- We see that the only massless part of the connection is A(N−4,−), describing a “purely internal” O(N − 4) Yang-Mills field. All other fields have acquired a mass of the order of Planck’s mass. The fa... |

1 | e-Print: arXiv:0712.0977 [hep-th] has proposed a generalization of the Plebanski action that could be used in these unified theories. As an example he applies it to a model with gauge group SO(8). This action admits solutions that describe either the symm - Smolin |