Is Barbero's Hamiltonian formulation a gauge theory of Lorentzian gravity?

Samuel, Joseph

doi:10.1088/0264-9381/17/20/101

Cited by 87 publications

(126 citation statements)

References 21 publications

(43 reference statements)

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“…Coming back to the case at hand, I do not know of a uniqueness result that does not make the assumptions concerning the spacetime interpretation of the generators H (α, β). Compare also the related discussion in [66,67].…”

Section: Uniqueness Of Einstein's Geometrodynamics It Is Sometimes Stmentioning

confidence: 80%

“…Also, unless the Barbero-Immirzi parameter takes the very special values ±i (for Lorentzian signature; ±1 for Euclidean signature) the connection variable does not admit an interpretation as a space-time gauge field restricted to spacelike hypersurfaces (cf. [42,67]). For example, the holonomy of a spacelike curve γ varies with the choice of the spacelike hypersurface containing γ , which would be impossible if the spatial connection were the restriction of a space-time connection [67].…”

Section: And R(h) Is the Ricci Scalar Of (H σ) Note That (34) Is Jumentioning

confidence: 99%

“…[42,67]). For example, the holonomy of a spacelike curve γ varies with the choice of the spacelike hypersurface containing γ , which would be impossible if the spatial connection were the restriction of a space-time connection [67]. Accordingly, the dynamics generated by the constraints does then not admit the interpretation of being induced by appropriately moving a hypersurface through a spacetime with fixed geometric structures on it.…”

Section: And R(h) Is the Ricci Scalar Of (H σ) Note That (34) Is Jumentioning

confidence: 99%

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The Superspace of geometrodynamics

Giulini

2009

Gen Relativ Gravit

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Section: Uniqueness Of Einstein's Geometrodynamics It Is Sometimes Stmentioning

confidence: 80%

Section: And R(h) Is the Ricci Scalar Of (H σ) Note That (34) Is Jumentioning

confidence: 99%

Section: And R(h) Is the Ricci Scalar Of (H σ) Note That (34) Is Jumentioning

confidence: 99%

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The Superspace of geometrodynamics

Giulini

2009

Gen Relativ Gravit

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“…In LQG, the Ashtekar-Barbero connection is not a spacetime connection [7]. Further, there exists no corresponding connection operator in the quantum theory.…”

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confidence: 99%

Covariant effective action for loop quantum cosmology à la Palatini

Olmo

Singh

2009

J. Cosmol. Astropart. Phys.

121

130

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In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a continuum description in terms of an effective Hamiltonian. Here we provide an algorithm to obtain the corresponding effective action, establishing in this way the covariance of the theory for the first time. This result provides new insights on the continuum properties of the discrete structure of quantum geometry and opens new avenues to extract physical predictions such as those related to gauge invariant cosmological perturbations.Understanding the nature of gravity and spacetime at high energies is one of the most interesting open issues in theoretical physics. In it lie the answers to various questions which Einstein's theory of general relativity (GR) fails to address, such as the origin of our Universe and the resolution of the big bang singularity. This is also deeply connected with our understanding of the way various dynamical and structural properties of the spacetime and the field equations, such as covariance, emerge from a more fundamental description.It is generally believed that limitations of GR would be overcome in a quantum theory of gravity, which is expected to cure the big bang singularity and provide modifications to the Friedman dynamics in the early universe. An approach in this direction is to find a renormalizable perturbative theory of quantum gravity which agrees with GR at low energies. This inspired modifications of the Einstein-Hilbert action via addition of terms involving higher curvature invariants and higher derivatives of the metric, motivating ansatzes to potentially tame the initial singularity (see for example [1]). They inevitably have more degrees of freedom than GR and often face limitations such as lack of unitarity, ghosts, and instabilities. These effective theories are based on a classical continuum spacetime and are covariant by construction.To faithfully capture the dynamical nature of spacetime, however, we need to go beyond the perturbative methods. One such approach is loop quantum gravity, which is background independent and non-perturbative [2]. It is a canonical quantization of gravity with classical phase space given by the Ashtekar variables: the connection A i a and the triad E a i . A key prediction of the theory is the discreteness of the eigenvalues of geometrical operators such as volume and area. Thus, the classical notion of a smooth differentiable geometry is replaced by a discrete quantum geometry. Techniques of LQG have been successfully applied to formulate loop quantum cosmology (LQC) which is a non-perturbative quantization of cosmological spacetimes [3]. In recent years, extensive analytical work and numerical simulations have shown that the big bang singularity can be resolved in LQC. The non-perturbative quantum geometric effects result in a quantum bounce to a pre-big bang branch when the energy density o...

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“…If the configuration space encompassing all degrees of freedom is compact then the topology suggests a unique choice: the physical state should be described by a constant wave function on the neglected degrees of freedom. However, in a general case of a non-compact 6 It turns out that in the non-compact case it is possible to use an orthogonal sum to 'glue' the spaces {Hγ } [18] into a large Hilbert space, but then there exist obstacles [11] which do not allow us to define any acceptable representation of classical observables on the large Hilbert space. 7 The original text in Polish was translated into English by this author.…”

Section: Projective Techniquesmentioning

confidence: 99%

Quantization of Diffeomorphism Invariant Theories of Connections with a Non-Compact Structure Group—an Example

Okołów

2009

Commun. Math. Phys.

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A simple diffeomorphism invariant theory of connections with the non-compact structure group R of real numbers is quantized. The theory is defined on a fourdimensional 'space-time' by an action resembling closely the self-dual Plebański action for general relativity. The space of quantum states is constructed by means of projective techniques by Kijowski [1]. Except this point the applied quantization procedure is based on Loop Quantum Gravity methods.

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Is Barbero's Hamiltonian formulation a gauge theory of Lorentzian gravity?

Cited by 87 publications

References 21 publications

The Superspace of geometrodynamics

The Superspace of geometrodynamics

Covariant effective action for loop quantum cosmology à la Palatini

Quantization of Diffeomorphism Invariant Theories of Connections with a Non-Compact Structure Group—an Example

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