Manifestly Lorentz-covariant variables for the phase space of general relativity

We carry out the canonical analysis of the n-dimensional Palatini action with or without a cosmological constant (n ≥ 3) introducing neither second-class constraints nor resorting to any gauge fixing. This is accomplished by providing an expression for the spatial components of the connection that allows us to isolate the nondynamical variables present among them, which can later be eliminated from the action by using their own equation of motion. As a result, we obtain the description of the phase space of general relativity in terms of manifestly SO(n − 1, 1) [or SO(n)] covariant variables subject to first-class constraints only, with no second-class constraints arising during the process. Afterwards, we perform, at the covariant level, a canonical transformation to a set of variables in terms of which the above constraints take a simpler form. Finally, we impose the time gauge and make contact with the SO(n − 1) ADM formalism.I.

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“…This formulation was also obtained after applying a canonical transformation on the Hamiltonian theory resulting from the Holst action [10].…”

Section: Canonical Transformationsmentioning

confidence: 99%

Canonical analysis ofn-dimensional Palatini action without second-class constraints

et al. 2020

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“…[8]. In this way, we establish that the manifestly Lorentz-covariant canonical formulation of general relativity involving only first-class constraints [14,15] can also be derived, without introducing second-class constraints in the process, from the formulation of general relativity as a constrained BF theory with Immirzi parameter and a cosmological constant.…”

Section: Introductionmentioning

confidence: 78%

“…[15], resulting in the manifestly Lorentz-covariant formulation embodied in (41), whose relation to other canonical formulations of general relativity was established in Refs. [14,15] (see also Ref. [21]).…”

Section: Discussionmentioning

confidence: 99%

Canonical analysis with no second-class constraints of BF gravity with Immirzi parameter

Montesinos

Celada

2020

Phys. Rev. D

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In this paper we revisit the canonical analysis of BF gravity with the Immirzi parameter and a cosmological constant. By examining the constraint on the B field, we realize that the analysis can be performed in a Lorentz-covariant fashion while utterly avoiding the introduction of second-class constraints during the whole process. Finally, we make contact with the description of the phase space of first-order general relativity in terms of canonical variables with manifest Lorentz covariance subject to first-class constraints only recently introduced.I.

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“…Because Lorentz invariance plays a fundamental role in modern physics, there have been different approaches tackling the Lorentz-covariant canonical analysis of the Holst action. Nonetheless, those perspectives introduce second-class constraints, which are dealt with at the end either by using the Dirac bracket [9] or by solving them explicitly [10][11][12][13]. Remarkably, in Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Remarkably, in Refs. [11,12] the second-class constraints were solved while preserving the manifest Lorentz invariance of the theory, obtaining different sets of canonical variables for the phase space of general relativity that is now described by first-class constraints only.…”

Section: Introductionmentioning

confidence: 99%

Canonical analysis of Holst action without second-class constraints

2020

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We perform the canonical analysis of the Holst action for general relativity with a cosmological constant without introducing second-class constraints. Our approach consists in identifying the dynamical and nondynamical parts of the involved variables from the very outset. After eliminating the nondynamical variables associated with the connection, we obtain the description of phase space in terms of manifestly SO(3, 1) [or SO(4), depending on the signature] covariant canonical variables and first-class constraints only. We impose the time gauge on them and show that the Ashtekar-Barbero formulation of general relativity emerges. Later, we discuss a family of canonical transformations that allows us to construct new SO(3, 1) [or SO(4)] covariant canonical variables for the phase space of the theory and compare them with the ones already reported in the literature, pointing out the presence of a set of canonical variables not considered before. Finally, we resort to the time gauge again and find that the theory, when written in terms of the new canonical variables, either collapses to the SO(3) ADM formalism or to the Ashtekar-Barbero formalism with a rescaled Immirzi parameter.

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Manifestly Lorentz-covariant variables for the phase space of general relativity

Cited by 18 publications

References 34 publications

Canonical analysis ofn-dimensional Palatini action without second-class constraints

Canonical analysis ofn-dimensional Palatini action without second-class constraints

Canonical analysis with no second-class constraints of BF gravity with Immirzi parameter

Canonical analysis of Holst action without second-class constraints

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