Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum mechanics of fermion confined to a curved surface in
  Foldy-Wouthuysen representation   In Foldy-Wouthuysen representation, we deduce the effective quantum mechanics
for a particle confined to a curved surface by using the thin-layer
quantization scheme. We find that the spin effect caused by confined potential
as the results of relativistic correction in the non-relativistic limit.
Furthermore, the spin connection appeared in curved surface which depends on
curvature contributes a Zeeman-like gap in the relativistic correction term. In
addition, the confined potential also induces a curvature-independent energy
shift, which is from the zitterbewegung effect. As an example, we apply the
effective Hamiltonian to torus surface, in which we obtain expectantly the spin
effects related to confined potential. Those results directly demonstrate the
scaling of the uncommutation of the non-relativistic limit and the thin-layer
quantization formalism

21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th