Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak value picture on quantum observables: gauge-invariant vector
  potentials   The conservation of physical quantities under coordinate transformations,
known as gauge invariance, has been the foundation of theoretical frameworks in
both quantum and classical theory. The finding of gauge-invariant quantities
has enabled the geometric and topological interpretations of quantum phenomena
with the Berry phase, or the separation of quark and gluon contributions in
quantum chromodynamics. Here, with an example of quantum geometric
quantities-Berry connection, phase, and curvature-we extract a new
gauge-invariant quantity by applying a "weak value picture". By employing
different pre- and post-selections in the derivation of the Berry phase in the
context of weak values, we derive the gauge-invariant vector potential from the
Berry connection that is originally gauge-dependent, and show that the obtained
vector potential corresponds to the weak value of the projected momentum
operator. The local nature of this quantity is demonstrated with an example of
the Aharonov-Bohm effect, proving that this gauge-invariant vector potential
can be interpreted as the only source of the Berry curvature in the magnetic
field. This weak value decomposition approach will lead to the extraction of
new measurable quantities from traditionally unobservable quantities.

21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin