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F. Fiorini, P. A. González, and Y. Vásquez, Compact extra dimensions in cosmologies with f ⁡ ( T ) f(T) structure, Phys. Rev. D 89
Original
1912
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R. Ferraro and F. Fiorini, On Born-Infeld Gravity in Weitzenbock spacetime, Phys. Rev. D 78
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J. W. Maluf and J. F. da Rocha-Neto, General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry, Gen. Relativ. Gravit. 31
1999
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J. W. Maluf and J. F. da Rocha-Neto, Hamiltonian formulation of general relativity in the teleparallel geometry, Phys. Rev. D 64
2001
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R. Ferraro and F. Fiorini, Modified teleparallel gravity: Inflation without inflaton, Phys. Rev
2007
Earlier work this paper cites.

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2018

Hamiltonian formalism for f(T) gravity

Ferraro, Rafael, Guzmán, María José

Understand

We present the Hamiltonian formalism for $f(T)$ gravity, and prove that the theory has $\frac{n(n-3)}{2}+1$ degrees of freedom (d.o.f.) in $n$ dimensions.

We start from a scalar-tensor action for the theory, which represents a scalar field minimally coupled with the torsion scalar $T$ that defines the teleparallel equivalent of general relativity (TEGR) Lagrangian.
$T$ is written as a quadratic form of the coefficients of anholonomy of the vierbein.
We obtain the primary constraints through the analysis of the structure of the eigenvalues of the multi-index matrix involved in the definition of the canonical momenta.

Built on

F. Fiorini, P. A. González, and Y. Vásquez, Compact extra dimensions in cosmologies with f ⁡ ( T ) f(T) structure, Phys. Rev. D 89
Original
1912
Earlier work this paper cites.
H. Weyl, Das Relativitätsprinzip, Fortschritte der Mathematischen Wissenschaften in Monographien
1918
Earlier work this paper cites.
E. Cartan, Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion, C.R. Hebd. Seances Acad. Sci. 174
1922
Earlier work this paper cites.
E. Cartan, Sur les espaces généralisés et la théorie de la Relativité, C.R. Hebd. Seances Acad. Sci. 174
1922
Earlier work this paper cites.
R. Weitzenböck, Invarianten theorie
1923
Earlier work this paper cites.
A. Einstein, Einheitliche Feldtheorie der Gravitation und Elektrizität, Pruess. Akad. Wiss. 414
1925
Earlier work this paper cites.
A. Einstein, Sitzungsberichte der Preussischen Akademie der Wissenschaften
1928
Earlier work this paper cites.
A. Einstein, Zur Theorie der Räume mit Riemannmetrik und Fernparallelismus, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 401
1930
Earlier work this paper cites.
A. Einstein, Auf die Riemann-Metrik und den Fern-Parallelismus gegründete einheitliche Feldtheorie, Math. Ann. 102
1930
Earlier work this paper cites.
J. L. Anderson and P. G. Bergmann, Constraints in covariant field theories, Phys. Rev. 83
1951
Earlier work this paper cites.
P. A. M. Dirac, Lectures on quantum mechanics
1964
Earlier work this paper cites.
Y. M. Cho, Einstein Lagrangian as the translational Yang-Mills Lagrangian, Phys. Rev. D 14
1976
Earlier work this paper cites.
R. Ferraro and F. Fiorini, On Born-Infeld Gravity in Weitzenbock spacetime, Phys. Rev. D 78
Original
1981
Earlier work this paper cites.
K. Hayashi and T. Shirafuji, New general relativity, Phys. Rev. D 19
1981
Earlier work this paper cites.
K. Sundermeyer, Constrained dynamics with applications to Yang-Mills theory, general relativity, classical spin, dual string model, Lect. Notes Phys. 169
1982
Earlier work this paper cites.
M. Henneaux and C. Teitelboim, Quantization of gauge systems
1992
Earlier work this paper cites.
J. W. Maluf and J. F. da Rocha-Neto, General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry, Gen. Relativ. Gravit. 31
1999
Earlier work this paper cites.
J. W. Maluf and J. F. da Rocha-Neto, Hamiltonian formulation of general relativity in the teleparallel geometry, Phys. Rev. D 64
2001
Earlier work this paper cites.
R. Ferraro and F. Fiorini, Modified teleparallel gravity: Inflation without inflaton, Phys. Rev
2007
Earlier work this paper cites.