Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge fields, point interactions and few-body problems in one dimension   Point interactions for the second derivative operator in one dimension are
studied. Every operator from this family is described by the boundary
conditions which include a $ 2 \times 2 $ real matrix with the unit determinant
and a phase. The role of the phase parameter leading to unitary equivalent
operators is discussed in the present paper. In particular it is shown that the
phase parameter is not redundant (contrary to previous studies) if non
stationary problems are concerned. It is proven that the phase parameter can be
interpreted as the amplitude of a singular gauge field. Considering the
few-body problem we extend the range of parameters for which the exact solution
can be found using the Bethe Ansatz.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat