scholarly journals Gravity from Poincare Gauge Theory of the Fundamental Particles. III: Weak Field Approximation

1980 ◽  
Vol 64 (4) ◽  
pp. 1435-1452 ◽  
Author(s):  
K. Hayashi ◽  
T. Shirafuji
Keyword(s):  
Gauge Theory ◽  
Field Approximation ◽  
Weak Field ◽  
Fundamental Particles ◽  
Weak Field Approximation

The Einstein–Maxwell-particle system in the York canonical basis of ADM tetrad gravity. Part 2. The weak field approximation in the 3-orthogonal gauges and Hamiltonian post-minkowskian gravity: the N-body problem and gravitational waves with asymptotic background 1This paper is one of three companion papers published in the same issue of Can. J. Phys.

2012 ◽  
Vol 90 (11) ◽  
pp. 1077-1130 ◽  
Author(s):  
David Alba ◽  
Luca Lusanna
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Waves ◽  
Particle System ◽  
Canonical Basis ◽  
Field Approximation ◽  
Weak Field ◽  
N Body Problem ◽  
Hamilton Equations ◽  
Weak Field Approximation ◽  
Tetrad Gravity

In this second paper we define a post-minkowskian (PM) weak field approximation leading to a linearization of the Hamilton equations of Arnowitt–Deser–Misner (ADM) tetrad gravity in the York canonical basis in a family of nonharmonic 3-orthogonal Schwinger time gauges. The York time 3K (the relativistic inertial gauge variable, not existing in newtonian gravity, parametrizing the family, and connected to the freedom in clock synchronization, i.e., to the definition of the the shape of the instantaneous 3-spaces) is set equal to an arbitrary numerical function. The matter are considered point particles, with a Grassmann regularization of self-energies, and the electromagnetic field in the radiation gauge: an ultraviolet cutoff allows a consistent linearization, which is shown to be the lowest order of a hamiltonian PM expansion. We solve the constraints and the Hamilton equations for the tidal variables and we find PM gravitational waves with asymptotic background (and the correct quadrupole emission formula) propagating on dynamically determined non-euclidean 3-spaces. The conserved ADM energy and the Grassmann regularization of self-energies imply the correct energy balance. A generalized transverse–traceless gauge can be identified and the main tools for the detection of gravitational waves are reproduced in these nonharmonic gauges. In conclusion, we get a PM solution for the gravitational field and we identify a class of PM Einstein space–times, which will be studied in more detail in a third paper together with the PM equations of motion for the particles and their post-newtonian expansion (but in the absence of the electromagnetic field). Finally we make a discussion on the gauge problem in general relativity to understand which type of experimental observations may lead to a preferred choice for the inertial gauge variable 3K in PM space–times. In the third paper we will show that this choice is connected with the problem of dark matter.

QUANTUM FIELDS WITH MODIFIED DISPERSION RELATIONS IN CURVED SPACES

2011 ◽  
Vol 20 (05) ◽  
pp. 745-756 ◽  
Author(s):  
FRANCISCO DIEGO MAZZITELLI
Keyword(s):  
Vector Field ◽  
General Structure ◽  
Scalar Fields ◽  
Field Approximation ◽  
Weak Field ◽  
Dispersion Relations ◽  
Quantum Fields ◽  
Renormalization Procedure ◽  
Modified Dispersion Relations ◽  
Weak Field Approximation

We discuss the renormalization procedure for quantum scalar fields with modified dispersion relations in curved spacetimes. We consider two different ways of introducing modified dispersion relations: through the interaction with a dynamical temporal vector field, as in the context of the Einstein–Aether theory, and breaking explicitly the covariance of the theory, as in Hǒrava–Lifshitz gravity. Working in the weak field approximation, we show that the general structure of the counterterms depends on the UV behavior of the dispersion relations and on the mechanism chosen to introduce them.

scholarly journals Spectral Action Beyond the Weak-Field Approximation

2012 ◽  
Vol 316 (3) ◽  
pp. 595-613 ◽  
Author(s):  
B. Iochum ◽  
C. Levy ◽  
D. Vassilevich
Keyword(s):  
Field Approximation ◽  
Weak Field ◽  
Spectral Action ◽  
Weak Field Approximation

scholarly journals Massive Conformal Gravity

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
F. F. Faria
Keyword(s):  
Scalar Field ◽  
Field Approximation ◽  
Weak Field ◽  
Vacuum Field ◽  
Conformal Transformations ◽  
Conformal Gravity ◽  
Field Equations ◽  
Metric Tensor ◽  
Weak Field Approximation ◽  
Massive Theory

We construct a massive theory of gravity that is invariant under conformal transformations. The massive action of the theory depends on the metric tensor and a scalar field, which are considered the only field variables. We find the vacuum field equations of the theory and analyze its weak-field approximation and Newtonian limit.

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