Nonlinear Hamiltonian analysis of new quadratic torsion theories: Cases with curvature-free constraints

Barker, W. E. V.; Lasenby, A.; Hobson, M.; Handley, Will

doi:10.1103/physrevd.104.084036

Cited by 11 publications

(35 citation statements)

References 32 publications

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“…To whatever extent this is true, strong coupling will be fatal to the more general PGTs. We confirmed in [15] that the problem extends also into linearly viable cases for which ̂ 0 = 0.…”

Section: Introductionsupporting

confidence: 63%

“…In order to efficiently and thoroughly discuss the new general theory (4), we must create a more formal notation than that previously used in [15]. We use (as in Eqs.…”

Section: A Developing the Formalismmentioning

confidence: 99%

“…Note some further identities ℎ ≡ and ℎ ≡ . As set out in [15], the overbar on an index, and the (⟂) symbol, refer to indices perpendicular and parallel to the ADM unit vector . For a discussion of the ADM formulation of PGT with these exact same conventions, see [5,15].…”

Section: A Developing the Formalismmentioning

confidence: 99%

“…The basic units of the 'particle physics' formulation of PGT [5,10,[14][15][16] are the translational and rotational gauge fields and = [ ] , where Greek indices are holonomic, referring to coordinates on a flat and torsion-free reference background , and Roman indices are Lorentzian. In the alternative 'geometric' formulation, these gauge fields are reimagined as the tetrad and spin-connection ≡ [ ] , while the spacetime enjoys an intrinsic curvature and torsion [5,17].…”

Section: Introductionmentioning

confidence: 99%

“…In Section IV we perform the canonical analysis of the 1 + torsional mode with a simple choice of multiplier. Conclusions follow in Section V. Most of our conventions and notation, especially for the Hamiltonian, ADM or 3 + 1 structure of the PGT, are in common with [15,16], and with the companion paper in [27]; these conventions are in turn derived from [5,23,24]. We use the 'West Coast' signature (+, −, −, −).…”

Section: Introductionmentioning

confidence: 99%

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Geometric multipliers and partial teleparallelism in Poincaré gauge theory

Barker¹

2022

Preprint

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The dynamics of the torsion-powered teleparallel theory are only viable because thirty-six multiplier fields disable all components of the Riemann-Cartan curvature. We generalise this suggestive approach by considering Poincaré gauge theory in which sixty such 'geometric multipliers' can be invoked to disable any given irreducible part of the curvature, or indeed the torsion. Torsion theories motivated by a weak-field analysis frequently suffer from unwanted dynamics in the strong-field regime, such as the activation of ghosts. By considering the propagation of massive, parity-even vector torsion, we explore how geometric multipliers may be able to limit strong-field departures from the weak-field Hamiltonian constraint structure, and consider their tree-level phenomena.

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“…To whatever extent this is true, strong coupling will be fatal to the more general PGTs. We confirmed in [15] that the problem extends also into linearly viable cases for which ̂ 0 = 0.…”

Section: Introductionsupporting

confidence: 63%

“…In order to efficiently and thoroughly discuss the new general theory (4), we must create a more formal notation than that previously used in [15]. We use (as in Eqs.…”

Section: A Developing the Formalismmentioning

confidence: 99%

Section: A Developing the Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Geometric multipliers and partial teleparallelism in Poincaré gauge theory

Barker¹

2022

Preprint

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Weyl-invariant Einstein-Cartan gravity: unifying the strong CP and hierarchy puzzles

Karananas,

Shaposhnikov,

Zell

2024

J. High Energ. Phys.

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We show that the minimal Weyl-invariant Einstein-Cartan gravity in combination with the Standard Model of particle physics contains just one extra scalar degree of freedom (in addition to the graviton and the Standard Model fields) with the properties of an axion-like particle which can solve the strong CP-problem. The smallness of this particle’s mass as well as of the cosmological constant is ensured by tiny values of the gauge coupling constants of the local Lorentz group. The tree value of the Higgs boson mass and that of Majorana leptons (if added to the Standard Model to solve the neutrino mass, baryogenesis and dark matter problems) are very small or vanishing, opening the possibility of their computability in terms of the fundamental parameters of the theory due to nonperturbative effects.

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Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group

Nikjoo,

Zlosnik

2024

Class. Quantum Grav.

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A number of approaches to gravitation have much in common with the gauge theories of the standard model of particle physics. In this paper, we develop the Hamiltonian formulation of a class of gravitational theories that may be regarded as spontaneously-broken gauge theories of the complexified Lorentz group $SO(1,3)_C$ with the gravitational field described entirely by a gauge field valued in the Lie algebra of $SO(1,3)_C$ and a `Higgs field' valued in the group's fundamental representation. The theories have one free parameter $\beta$ which appears in a similar role to the inverse of the Barbero-Immirzi parameter of Einstein-Cartan theory. However, contrary to that parameter, it is shown that the number of degrees of freedom crucially depends on the value of $\beta$. For non-zero values of $\beta$, it is shown the theories possesses three complex degrees of freedom, and for the specific values $\beta=\pm i$ an extension to General Relativity is recovered in a symmetry-broken regime. For the value $\beta=0$, the theory possesses no local degrees of freedom. A non-zero value of $\beta$ corresponds to the self-dual and anti-self-dual gauge fields appearing asymmetrically in the action, therefore in these models, the existence of gravitational degrees of freedom is tied to chiral asymmetry in the gravitational sector.

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Nonlinear Hamiltonian analysis of new quadratic torsion theories: Cases with curvature-free constraints

Cited by 11 publications

References 32 publications

Geometric multipliers and partial teleparallelism in Poincaré gauge theory

Geometric multipliers and partial teleparallelism in Poincaré gauge theory

Weyl-invariant Einstein-Cartan gravity: unifying the strong CP and hierarchy puzzles

Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group

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