Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase theory and critical exponents for the Tomonaga-Luttinger model
  with harmonic confinement   A phase operator formulation for a recent model of interacting
one-dimensional fermions in a harmonic trap is developed. The resulting theory
is similar to the corresponding approach for the Luttinger model with open
boundary conditions (OBC). However, in place of the spatial coordinate $z$, a
dimensionless variable $u$ defined on the unit circle appears as argument of
the phase fields and $u$ is non-linearly related to $z$. Furthermore, form
factors appear which reflect the harmonic trap geometry. The theory is applied
to calculate one-particle correlation functions. In a properly defined
thermodynamic limit, bulk and boundary critical exponents are calculated for
the static two-point correlation function and the dynamic local correlation
function. The local spectral density is also considered. The critical exponents
found are in agreement with those known for OBC with the exception of the
boundary scaling exponent $\Delta_\perp$.

31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math