Gauge connection formulations for general relativity

González, Diego López; Montesinos, Merced

doi:10.1103/physrevd.91.024021

Cited by 4 publications

(7 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By eliminating auxiliary fields in Plebanski's action, it is possible to derive interesting alternative formulations of general relativity. Such is the case of the CDJ formulation [20,21], the pure connection formulation [25], and the gauge connection formulations of [79]. The aim of this section is to review how these formulations emerge from the Plebanski formulation.…”

mentioning

confidence: 99%

BF gravity

Celada

González

Montesinos

2016

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

BF gravity comprises all the formulations of gravity that are based on deformations of BF theory. Such deformations consist of either constraints or potential terms added to the topological BF action that turn some of the gauge degrees of freedom into physical ones, particularly giving rise to general relativity. The BF formulations have provided new and deep insights into many classical and quantum aspects of the gravitational field, setting the foundations for the approach to quantum gravity known as spinfoam models. In this review, we present a self-contained and unified treatment of the BF formulations of D-dimensional general relativity and other related models, focusing on the classical aspects of them and including some new results.

show abstract

mentioning

confidence: 99%

BF gravity

Celada

González

Montesinos

2016

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the other hand, notice that Plebanski's action emerges from ( 79) when B i is integrated out. Indeed, the variation with respect to B i leads to B i = Σ i , which in turn substituted into (79) gives precisely Plebanski's action (6), thus concluding our procedure. It is important to emphasize that (6) works well for both Λ = 0 and Λ = 0, and that its equivalence with the pure connection action (74) holds whenever X is invertible and Λ = 0.…”

Section: 17mentioning

confidence: 65%

“…where f ′ = df /dTrΨ, the action (76) describes general relativity [79]. In particular, these properties are enjoyed by f = α 1 (2TrΨ + Λ) + α 2 (TrΨ + Λ) 2 if the constants α 1 and α 2 are such that α 1 = 0 and α 1 + α 2 Λ = 0 with Λ = 0 or Λ = 0.…”

Section: Canonical Analysismentioning

confidence: 99%

$BF$ gravity

Celada,

González,

Montesinos

2016

Preprint

Self Cite

View full text Add to dashboard Cite

BF gravity comprises all the formulations of gravity that are based on deformations of BF theory. Such deformations consist of either constraints or potential terms added to the topological BF action that turn some of the gauge degrees of freedom into physical ones, particularly giving rise to general relativity. The BF formulations have provided new and deep insights into many classical and quantum aspects of the gravitational field, setting the foundations for the approach to quantum gravity known as spinfoam models. In this review, we present a self-contained and unified treatment of the BF formulations of Ddimensional general relativity and other related models, focusing on the classical aspects of them and including some new results.

show abstract

“…(iii) In the context of the formulations explored in Ref. [23], the action principle (15) (iv) For λ = 0 and β = 0, the action (1) describes conformally anti-self-dual gravity. In fact, by eliminating the B field and ρ from it, we arrive at the action of Ref.…”

Section: Discussionmentioning

confidence: 99%

Plebanski-like action for general relativity and anti-self-dual gravity

2016

Self Cite

View full text Add to dashboard Cite

We present a new $BF$-type action for complex general relativity with or without a cosmological constant resembling Plebanski's action, which depends on an SO(3,$\mathbb{C}$) connection, a set of 2-forms, a symmetric matrix, and a 4-form. However, it differs from the Plebanski formulation in the way that the symmetric matrix enters into the action. The advantage of this fact is twofold. First, as compared to Plebanski's action, the symmetric matrix can now be integrated out, which leads to a pure $BF$-type action principle for general relativity; the canonical analysis of the new action then shows that it has the same phase space of the Ashtekar formalism up to a canonical transformation induced by a topological term. Second, a particular choice of the parameters involved in the formulation produces a $BF$-type action principle describing conformally anti-self-dual gravity. Therefore, the new action unifies both general relativity and anti-self-dual gravity.Comment: 6 pages, accepted for publication in Physical Review

show abstract

Gauge connection formulations for general relativity

Cited by 4 publications

References 22 publications

BF gravity

BF gravity

$BF$ gravity

Plebanski-like action for general relativity and anti-self-dual gravity

Contact Info

Product

Resources

About