Hamiltonian formalism for f (T) gravity

We present the Hamiltonian formalism for f(T) gravity, and prove that the theory has 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 e...

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Publicado: 2018
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_24700010_v97_n10_p_Ferraro
http://hdl.handle.net/20.500.12110/paper_24700010_v97_n10_p_Ferraro
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_24700010_v97_n10_p_Ferraro2023-06-08T16:36:35Z Hamiltonian formalism for f (T) gravity We present the Hamiltonian formalism for f(T) gravity, and prove that the theory has 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. The auxiliary scalar field generates one extra primary constraint when compared with the TEGR case. The secondary constraints are the super-Hamiltonian and supermomenta constraints, that are preserved from the Arnowitt-Deser-Misner formulation of GR. There is a set of n(n-1)2 primary constraints that represent the local Lorentz transformations of the theory, which can be combined to form a set of n(n-1)2-1 first-class constraints, while one of them becomes second class. This result is irrespective of the dimension, due to the structure of the matrix of the brackets between the constraints. The first-class canonical Hamiltonian is modified due to this local Lorentz violation, and the only one local Lorentz transformation that becomes second-class pairs up with the second-class constraint π≈0 to remove one d.o.f. from the n2+1 pairs of canonical variables. The remaining n(n-1)2+2n-1 primary constraints remove the same number of d.o.f., leaving the theory with n(n-3)2+1 d.o.f. This means that f(T) gravity has only one extra d.o.f., which could be interpreted as a scalar d.o.f. © 2018 American Physical Society. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_24700010_v97_n10_p_Ferraro http://hdl.handle.net/20.500.12110/paper_24700010_v97_n10_p_Ferraro
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We present the Hamiltonian formalism for f(T) gravity, and prove that the theory has 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. The auxiliary scalar field generates one extra primary constraint when compared with the TEGR case. The secondary constraints are the super-Hamiltonian and supermomenta constraints, that are preserved from the Arnowitt-Deser-Misner formulation of GR. There is a set of n(n-1)2 primary constraints that represent the local Lorentz transformations of the theory, which can be combined to form a set of n(n-1)2-1 first-class constraints, while one of them becomes second class. This result is irrespective of the dimension, due to the structure of the matrix of the brackets between the constraints. The first-class canonical Hamiltonian is modified due to this local Lorentz violation, and the only one local Lorentz transformation that becomes second-class pairs up with the second-class constraint π≈0 to remove one d.o.f. from the n2+1 pairs of canonical variables. The remaining n(n-1)2+2n-1 primary constraints remove the same number of d.o.f., leaving the theory with n(n-3)2+1 d.o.f. This means that f(T) gravity has only one extra d.o.f., which could be interpreted as a scalar d.o.f. © 2018 American Physical Society.
title Hamiltonian formalism for f (T) gravity
spellingShingle Hamiltonian formalism for f (T) gravity
title_short Hamiltonian formalism for f (T) gravity
title_full Hamiltonian formalism for f (T) gravity
title_fullStr Hamiltonian formalism for f (T) gravity
title_full_unstemmed Hamiltonian formalism for f (T) gravity
title_sort hamiltonian formalism for f (t) gravity
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_24700010_v97_n10_p_Ferraro
http://hdl.handle.net/20.500.12110/paper_24700010_v97_n10_p_Ferraro
_version_ 1768542480531193856

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