Degrees of freedom of f(T) gravity

• Published in: The journal of high energy physics Vol. 2011; no. 7
• Main Authors: Li, Miao, Miao, Rong-Xin, Miao, Yan-Gang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-07-2011; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Degrees of freedom; Elementary Particles; Fields (mathematics); Gravitation; High energy physics; Lorentz transformations; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; Scalars; String Theory; Classical Theories of Gravity; Cosmology of Theories beyond the SM
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2011)108

We investigate the Hamiltonian formulation of
f
(
T
) gravity and find that there are five degrees of freedom. The six first class constraints corresponding to the local Lorentz transformation in Teleparallel gravity become second class constraints in
f
(
T
) gravity, which leads to the appearance of three extra degrees of freedom and the violation of the local Lorentz invariance in
f
(
T
) gravity. In general, there are
D
 − 1 extra degrees of freedom for
f
(
T
) gravity in
D
dimensions, and this implies that the extra degrees of freedom correspond to one massive vector field or one massless vector field with one scalar field.