Gravitational Field as a Generalized Gauge Field

Yang–mills Gravity in Flat Space–time I: Classical Gravity With Translation Gauge Symmetry

“…[5,6,7,8,9, 10] As a result, the gauge symmetry, however powerful it may be, was unable to simplify the complicated interaction terms and, hence, the resultant theory of gravity had serious ultraviolet divergences and was not renormalizable. In view of this difficulty, we follow closely the Yang-Mills approach with a quadratic gauge-curvature and formulate the theory of Yang-Mills gravity on the basis of the translation gauge symmetry and flat space-time.…”

“…In the literature, when one arrives at this crucial step (10), [7,8,9,10] one usually gives up the Yang-Mills approach for a truly gauge invariant theory with a quadratic gauge curvature in a flat space-time, and follows Einstein's approach to discuss gravity by postulating Riemannian space-time due to the presence of φ µν or J µν in (11). In other words, one postulates E aα and G αβ in (11) as a real tetrad and a real metric tensor of physical space-time.…”

“…Thus, it is interesting to investigate the possibility of understanding gravity within the framework of the usual physical field theory, especially a framework with gauge symmetry in a flat space-time. An obvious challenge is to construct a gauge-invariant action (which involves quadratic gauge-curvature) in flat space-time that can produce the same good agreement with experimental results as those in general relativity (whose action involves linear space-time curvature [5,6,7,8,9,10,11]). …”

Poincaré gauge theory of gravity, gravitational interaction and regular accelerating universe

“…The distinctive feature of introduction of gravitational interaction on the base of the local gauge invariance principle unlike other fundamental physical interactions is the following: the gauge group in this case is connected with coordinates transformations and by their localization the geometrical structure of physical spacetime is changed. The metric gravitation theory can be introduced on the base of localization of 4-parametric translations group in Minkowski spacetime, invariance with respect to which leads according to Noether theorem to energy-momentum tensor and conservation laws of energy and momentum 2,3 . The introducing gauge field is connected with metric tensor of physical spacetime with the structure of pseudo-riemannian continuum.…”

The S-matrix and graviton self-energy in quantum Yang-Mills gravity

“…The idea of a gravitational theory with space-time translational gauge symmetry is very interesting from the viewpoint of Yang-Mills theory. It has attracted many authors [1,2,3] because the translational symmetry implies the conservation of energy-momentum tensor, which was supposed to be the source of the gravitational field. But most previous formulations were based on curved space-time and, hence, the problems of quantization and energy-momentum conservation remain unsolved.…”