On-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries

González, Barbero; Margalef-Bentabol, Juan; Varo, Valle; Villaseñor, Eduardo J. S.

doi:10.1103/physrevd.105.064066

Cited by 5 publications

(4 citation statements)

References 39 publications

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“…While Witten et al have found canonical and covariant formulations with symplectic structure, no Hamiltonian density was found [28][29][30][31][32]. Researchers have recently explored Witten's use of covariant, canonical, and symplectic structures in a wide range of gravitational theories, often referred to as covariant phase space methods [39][40][41][42]. DDW theory contains poly symplectic/multisymplectic geometry, which contains a Hamiltonian density and a conjugate poly momentum field.…”

Section: Appendix B Poly Koopman-von Neumann Mechanics As De Donder-w...mentioning

confidence: 99%

“…Ashtekar found a symplectic Hamiltonian density that used a hypersurface based on null infinity, but this was restricted to the study of general relativity [38]. Covariant phase space methods have been recently explored in a wide class of gravitational theories [39][40][41][42]. However, a comprehensive formulation of arbitrary field theory with a covariant, symplectic, and canonical Hamiltonian density still appears to be lacking to the best of our knowldge.…”

Section: Introductionmentioning

confidence: 99%

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Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density

Chester,

Arsiwalla,

Kauffman

et al. 2024

Symmetry

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We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman–von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize spacetime, energy–momentum, frequency–wavenumber, and the Fourier conjugate of energy–momentum. We clarify how first and second quantization can be found by simply mapping between operators in classical and quantum commutator algebras.

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Section: Appendix B Poly Koopman-von Neumann Mechanics As De Donder-w...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density

Chester,

Arsiwalla,

Kauffman

et al. 2024

Symmetry

View full text Add to dashboard Cite

show abstract

“…( 16) we observe that the generalized Ricci scalar reduces to the standard Ricci scalar on shell. Therefore, the classical action ( 10) is on-shell equivalent to the Einstein-Hilbert action of classical GR, see [39,44,45] for recent detailed discussions. Since each component A μ ∈ R, the Einstein-Hilbert-Palatini action has an R 4 gauge invariance.…”

Section: Einstein-hilbert-palatini Actionmentioning

confidence: 99%

Asymptotically safe Hilbert–Palatini gravity in an on-shell reduction scheme

Gies

Salek

2023

Eur. Phys. J. C

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We study the renormalization flow of Hilbert–Palatini gravity to lowest non-trivial order. We find evidence for an asymptotically safe high-energy completion based on the existence of an ultraviolet fixed point similar to the Reuter fixed point of quantum Einstein gravity. In order to manage the quantization of the large number of independent degrees of freedom in terms of the metric as well as the connection, we use an on-shell reduction scheme: for this, we quantize all degrees of freedom beyond Einstein gravity at a given order that remain after using the equations of motion at the preceding order. In this way, we can straightforwardly keep track of the differences emerging from quantizing Hilbert–Palatini gravity in comparison with Einstein gravity. To lowest non-trivial order, the difference is parametrized by fluctuations of an additional abelian gauge field. The critical properties of the ultraviolet fixed point of Hilbert–Palatini gravity are similar to those of the Reuter fixed point, occurring at a smaller Newton coupling and exhibiting more stable higher order exponents.

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“…In fact, in [57], the authors introduce the so-called "relative bicomplex framework" and develop a geometric formulation of the covariant phase space methods with boundaries, which is used to endow the space of solutions with (pre)symplectic structures. These ideas are used to discuss formulations of Palatini gravity, General Relativity and Holst theories in the presence of boundaries [4][5][6]. On the other hand, a classic research topic has been the relationship between finite and infinite dimensional approximation to Classical Field Theories (see Sect.…”

Section: Introductionmentioning

confidence: 99%

A new canonical affine bracket formulation of Hamiltonian classical field theories of first order

Gay-Balmaz,

Marrero,

Martínez Alba

2024

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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It has been a long standing question how to extend, in the finite-dimensional setting, the canonical Poisson bracket formulation from classical mechanics to classical field theories, in a completely general, intrinsic, and canonical way. In this paper, we provide an answer to this question by presenting a new completely canonical bracket formulation of Hamiltonian Classical Field Theories of first order on an arbitrary configuration bundle. It is obtained via the construction of the appropriate field-theoretic analogues of the Hamiltonian vector field and of the space of observables, via the introduction of a suitable canonical Lie algebra structure on the space of currents (the observables in field theories). This Lie algebra structure is shown to have a representation on the affine space of Hamiltonian sections, which yields an affine analogue to the Jacobi identity for our bracket. The construction is analogous to the canonical Poisson formulation of Hamiltonian systems although the nature of our formulation is linear-affine and not bilinear as the standard Poisson bracket. This is consistent with the fact that the space of currents and Hamiltonian sections are respectively, linear and affine. Our setting is illustrated with some examples including Continuum Mechanics and Yang–Mills theory.

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On-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries

Cited by 5 publications

References 39 publications

Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density

Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density

Asymptotically safe Hilbert–Palatini gravity in an on-shell reduction scheme

A new canonical affine bracket formulation of Hamiltonian classical field theories of first order

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