Gauge invariance in teleparallel gravity theories: A solution to the background structure problem

The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees of freedom in the Hamiltonian analysis. We show for general teleparallel theories of gravity, that fixing the gauge such that the spin connection vanishes in fact does not affect the counting of degrees of freedom. This manifests in the fact that the momenta of the Lorentz transformations which generate the spin connection are fully determined by the momenta of the tetrads.

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Hamiltonian of new general relativity using differential forms

International Journal of Modern Physics A ◽

10.1142/s0217751x2040014x ◽

2020 ◽

Vol 35 (02n03) ◽

pp. 2040014

Author(s):

Manuel Hohmann

Keyword(s):

General Relativity ◽

Recent Work ◽

Differential Forms ◽

Teleparallel Gravity ◽

Alternative Derivation ◽

Alternative Approach ◽

Gravity Theories

In a recent work we derived the kinematic Hamiltonian and primary constraints of the new general relativity class of teleparallel gravity theories and showed that these theories can be grouped in 9 classes, based on the presence or absence of primary constraints in their Hamiltonian. Here we demonstrate an alternative approach towards this result, by using differential forms instead of tensor components throughout the calculation. We prove that also this alternative derivation yields the same results and show how they are related to each other.

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Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss–Bonnet term

Classical and Quantum Gravity ◽

10.1088/1361-6382/aa93c8 ◽

2017 ◽

Vol 34 (23) ◽

pp. 235011 ◽

Cited By ~ 5

Author(s):

Álvaro de la Cruz-Dombriz ◽

Gabriel Farrugia ◽

Jackson Levi Said ◽

Diego Sáez-Chillón Gómez

Keyword(s):

Teleparallel Gravity ◽

Gravity Theories ◽

Bonnet Term

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SELF-DUAL FORMULATIONS OF d = 3 GRAVITY THEORIES IN THE PATH-INTEGRAL FRAMEWORK

International Journal of Modern Physics A ◽

10.1142/s0217751x11053377 ◽

2011 ◽

Vol 26 (14) ◽

pp. 2437-2459 ◽

Cited By ~ 2

Author(s):

P. J. ARIAS ◽

F. A. SCHAPOSNIK

Keyword(s):

Path Integral ◽

Fourth Order ◽

Gauge Invariance ◽

Vacuum Expectation ◽

Quantum Level ◽

Expectation Values ◽

Gravity Theories ◽

Dual Models

We study the connection, at the quantum level, between (d = 2+1)-dimensional self-dual models with actions of growing (from first to fourth) order, governing the dynamics of helicity ±2 massive excitations. We obtain identities between generating functionals of the different models using the path-integral framework, this allowing us to establish dual maps among relevant vacuum expectation values. We check consistency of these vacuum expectation values with the gauge invariance gained in each mapping.

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