Physics Of Gauge Fields In Quantum Nanosciences

We review the formulation of gauge fields in terms of the frame of reference as well as the space in which the frame is defined. We highlighted some recent applications of gauge physics in the momentum space - in the modern fields of the spin Hall effect, the magnon Hall, the optical Magnus and the graphene valley Hall. General procedures of gauge transformation which lead to the construction of the gauge curvature and the equations of motion (EOM) are outlined. Central to this review is our intention to illustrate the impact of gauge physics on the past and future development of many new research fields emerging out of condensed matter physics, particularly in quantum nanosciences and nanoelectronics.