Authors: Jean Pierre Rukundo
A unified Mathematical framework which describes particles interactions both in classical field theory of gravity and quantum field theory is presented, by introducing a velocity gauge field. The velocity gauge field Lagrangian is developed and shown to be equivalent to the Dirac field and related to the Electromagnetic field. The velocity fields interactions are shown to produce the Einstein-Hilbert action Lagrangian. Similar extension of the Mathematical framework to the Electromagnetic field produces the Quantum electrodynamics and Yang-Mills fields Lagrangians. Finally, a unified Lagrangian describing both velocity field and Electromagnetic field types is presented and alternative formulation suggested.
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