Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operators for the Aharonov-Anandan and Samuel-Bhandari Phases   We construct an operator for the Aharonov-Anandan phase for time independent
Hamiltonians. This operator is shown to generate the motion of cyclic quantum
systems through an equation of evolution involving only geometric quantities,
i.e. the distance between quantum states, the geometric phase and the total
length of evolution. From this equation, we derive an operator for the Samuel
and Bhandari phase (SB-phase) for non cyclic evolutions. Finally we show how
the SB-phase can be used to construct an operator corresponding to a quantum
clock which commutator with the Hamiltonian has a canonical expectation value.

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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: math
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg