GAUGE-INVARIANT REFERENCE SECTION AND GEOMETRIC PHASE

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