Poincaré-invariant Hamiltonian dynamics with a physical «common time»

Quantum Yang-Mills gravity in flat space-time and effective curved space-time for motions of classical objects

“…Because the simplicity of graviton's self-couplings in Yang-Mills gravity, we expect this theory to have a better high-energy behavior for the S-matrix. [31,32,33] These properties merit further study.…”

“…It appears impossible to adjust the three parameters a 1 , a 2 and a 3 in (58) to make S T G in (57) to be the same as S = L φ d 4 x in Yang-Mills gravity for both inertial and non-inertial frames. [4,1] In general, if the tetrad in a field theory involves dynamical fields, it will lead to complicated vertices in Feynman rules due to the presence of −det g µν in the action, if the field can be quantized.…”

“…The gravitational action (1) is written in inertial frames for simplicity of quantization and Feynman rules. However, the classical theory can be formulated in inertial and non-inertial frames (i.e., general frames with a metric tensor P µν [4]) with the gauge invariant action S φψ involving fermions and gravitational fields [1]…”

“…Yang-Mills gravity with Abelian group T(4) can be formulated in inertial and non-inertial frames. [1,4] The basic idea is a union of space-time symmetry and gauge symmetry in the following sense: For a general space-time symmetry of a physical system, let us consider the infinitesimal coordinate transformations,…”

“…This view leads to the Yang-Mills gravity with the local translational gauge symmetry based on the flat space-time with arbitrary coordinates (for general non-inertial frames). [1,4] The physics of Yang-Mills gravity turns out to be closely related to the gauge curvature C µνα of the translational group rather than the space-time curvature, where the gauge curvature involves a tensor gauge field φ µν .…”