Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Supersymmetry, Quantum Anomaly and Quasi-Exactly Solvable
  Systems   The nonlinear supersymmetry of one-dimensional systems is investigated in the
context of the quantum anomaly problem. Any classical supersymmetric system
characterized by the nonlinear in the Hamiltonian superalgebra is
symplectomorphic to a supersymmetric canonical system with the holomorphic form
of the supercharges. Depending on the behaviour of the superpotential, the
canonical supersymmetric systems are separated into the three classes. In one
of them the parameter specifying the supersymmetry order is subject to some
sort of classical quantization, whereas the supersymmetry of another extreme
class has a rather fictive nature since its fermion degrees of freedom are
decoupled completely by a canonical transformation. The nonlinear supersymmetry
with polynomial in momentum supercharges is analysed, and the most general
one-parametric Calogero-like solution with the second order supercharges is
found. Quantization of the systems of the canonical form reveals the two
anomaly-free classes, one of which gives rise naturally to the quasi-exactly
solvable systems. The quantum anomaly problem for the Calogero-like models is
``cured'' by the specific superpotential-dependent term of order $\hbar^2$. The
nonlinear supersymmetry admits the generalization to the case of
two-dimensional systems.

29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex