SYMMETRY STRUCTURES AND EXISTENCE CRITERIA OF GEOMETRIC PHASES

Origins of Berry's geometric phase are investigated and systematically categorized in terms of symmetry properties under time-reversal opera tions. Spontaneous time-reversal symmetry breaking of state vectors as well as explicitly time-reversal symmetry-violating Hamiltonians is s hown to given rise to the geometric phase. A topological singularity c an produce a quantized geometric phase without breaking the time-rever sal symmetry, but this case may also be understood within our general framework of classification. The unique role of the time-reversal oper ator among general antiunitary operators is discussed.