Gauge-invariant reference section and geometric phase

Abstract

We use a gauge-invariant 'reference section' and define the geometric phase for all quantum evolutions in a closed form. This geometric phase is obtained by integrating the inner product of the 'reference section' and its path derivative along the evolution curve which is valid for non-cyclic, non-unitary and non-Schrodinger evolutions of quantum systems. Two non-trivial examples are studied to realize our new expression.