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   Exact Abelian and Non-Abelian Geometric Phases  
نویسنده Soo C. ,Lin H.-C.
منبع Malaysian Journal Of Mathematical Sciences - 2014 - دوره : 8 - شماره : S - صفحه:85 -101
چکیده    The existence of hopf fibrations s2n+1/s1 = cpn and s4k+3/s3 = hpk allows us to treat the hilbert space of generic finite-dimensional quantum systems as the total bundle space with respectively u(1) and su(2) fibers and complex and quaternionic projective spaces as base manifolds. this alternative method of studying quantum states and their evolution reveals the intimate connection between generic quantum mechanical systems and geometrical objects. the exact abelian and non- abelian geometric phases,and more generally the geometrical factors for open paths,and their precise correspondence with geometric kähler and hyper-kähler connections will be discussed. explicit physical examples are used to verify and exemplify the formalism.
آدرس Department Of Physics,National Cheng Kung University, Taiwan, Department Of Physics,National Cheng Kung University, Taiwan

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