Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second quantized formulation of geometric phases   The level crossing problem and associated geometric terms are neatly
formulated by the second quantized formulation. This formulation exhibits a
hidden local gauge symmetry related to the arbitrariness of the phase choice of
the complete orthonormal basis set. By using this second quantized formulation,
which does not assume adiabatic approximation, a convenient exact formula for
the geometric terms including off-diagonal geometric terms is derived. The
analysis of geometric phases is then reduced to a simple diagonalization of the
Hamiltonian, and it is analyzed both in the operator and path integral
formulations. If one diagonalizes the geometric terms in the infinitesimal
neighborhood of level crossing, the geometric phases become trivial (and thus
no monopole singularity) for arbitrarily large but finite time interval $T$.
The integrability of Schr\"{o}dinger equation and the appearance of the
seemingly non-integrable phases are thus consistent. The topological proof of
the Longuet-Higgins' phase-change rule, for example, fails in the practical
Born-Oppenheimer approximation where a large but finite ratio of two time
scales is involved and $T$ is identified with the period of the slower system.
The difference and similarity between the geometric phases associated with
level crossing and the exact topological object such as the Aharonov-Bohm phase
become clear in the present formulation. A crucial difference between the
quantum anomaly and the geometric phases is also noted.

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The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
19
The categories of this paper are: eess
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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph