A group theoretic treatment of the geometric phase

We define a new unitary operator in the Hilbert space of a quantum system which parallel transports the state of the system along an arbitrary curve in the projective Hilbert space. This operator is geometrical even for an open curve in the sense that it depends uniquely only on the curve and is ind...

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Bibliographic Details
Published in:Physics letters. A 1992-04, Vol.164 (2), p.133-137
Main Authors: Sudarshan, E.C.G., Anandan, J., Govindarajan, T.R.
Format: Article
Language:English
Subjects:
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Physics
Quantum mechanics
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Summary:We define a new unitary operator in the Hilbert space of a quantum system which parallel transports the state of the system along an arbitrary curve in the projective Hilbert space. This operator is geometrical even for an open curve in the sense that it depends uniquely only on the curve and is independent of the Hamiltonian. Using this, when the curve is closed, the geometric phases discovered by Pancharatnam, Berry and Aharanov-Anandan are obtained.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(92)90691-E