J H Hannay 1998 J. Phys. A: Math. Gen. 31 L53 doi:10.1088/0305-4470/31/2/002
The Berry phase for spin in the Majorana representation
J H Hannay
Show affiliationsLETTER TO THE EDITOR
A continuous cyclic sequence of quantum states has an associated geometric, or Berry, phase 
. For spin J, such a sequence is described by a cyclic change in the 2J+1 coefficients 
of the basis states 
. The Berry phase is analysed here for the general case - that is, the coefficients are allowed to vary in an arbitrary cyclic manner. The result is expressed in geometric terms, specifically in the democratic representation due to Majorana. This uniquely characterizes the spin state 
, up to overall phase, by the positions of 2J dots on the unit sphere of directions in real space. If the positions are denoted by unit vectors 
, where 
, each traces out a parametrized loop on the sphere, and the Berry phase is given by an integral of combinations of these vectors.
- PACS
- MSC
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81Q70 Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
- Subjects
- Dates
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Issue 2 (16 January 1998)
Received 28 July 1997, in final form 26 September 1997
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The Berry phase for spin in the Majorana representation
J H Hannay 1998 J. Phys. A: Math. Gen. 31 L53
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