A Gauge Model for Gravity and considerations on the Asymmetry of Time and the SU (2) Mass Gap

A new formulation of the Hamiltonian formalism of general relativity is developed based on the adiabatic variation of the Hamiltonian constraint. This new formulation consists of complex valued anti-Hermitian 1- called the Berry gauge potentials. These are then used to develop the complex Berry-Einstein-Yang-Mills curvature 2- . The Berry-Yang-Mills field equations are then developed and interpreted in a novel manner to incorporate quantum temporal strings in the non-perturbative formalism. This is however just highlighted in this paper and will be pursued in another paper. Since, the holonomy phase construed is that of Lorentz rotation we perceive a new quantum structure of the space-time namely that of causality. The future light cones are soldered internally to the tensor fields naturally so that the Berry-Ehresmann connection defines a quantum gauge field of causality. This field evokes the causal structure attributed to space-time as gauge degrees of freedom of quantum space ― a fluid of future light cones. This symmetry being of the gauge field type has three generators i.e., three gauge bosons― all heavy and therefore attracted by gravity. Thus causality is a local gauge degree of freedom of gravity. Once the theory is developed, the problem of the mass gap is considered for our gauge field. It seems that the problem is solved in this paper.