184 research outputs found
Quasi-Exact Solvability in Local Field Theory. First Steps
The quantum mechanical concept of quasi-exact solvability is based on the
idea of partial algebraizability of spectral problem. This concept is not
directly extendable to the systems with infinite number of degrees of freedom.
For such systems a new concept based on the partial Bethe Ansatz solvability is
proposed. In present paper we demonstrate the constructivity of this concept
and formulate a simple method for building quasi-exactly solvable field
theoretical models on a one-dimensional lattice. The method automatically leads
to local models described by hermitian hamiltonians.Comment: LaTeX, 11 page
Non-linear Quantization of Integrable Classical Systems
It is demonstrated that the so-called "unavoidable quantum anomalies" can be
avoided in the farmework of a special non-linear quantization scheme. A simple
example is discussed in detail.Comment: LaTeX, 14 p
Quasi Exactly Solvable 22 Matrix Equations
We investigate the conditions under which systems of two differential
eigenvalue equations are quasi exactly solvable. These systems reveal a rich
set of algebraic structures. Some of them are explicitely described. An exemple
of quasi exactly system is studied which provides a direct counterpart of the
Lam\'e equation.Comment: 14 pages, Plain Te
Matching Weak Coupling and Quasiclassical Expansions For Dual QES Problems
Certain quasi-exactly solvable systems exhibit an energy reflection property
that relates the energy levels of a potential or of a pair of potentials. We
investigate two sister potentials and show the existence of this energy
reflection relationship between the two potentials. We establish a relationship
between the lowest energy edge in the first potential using the weak coupling
expansion and the highest energy level in the sister potential using a WKB
approximation carried out to higher order.Comment: 8 pages, 2 figures; typos correcte
A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure
Starting from a one-particle quasi-exactly solvable system, which is
characterized by an intrinsic sl(2) algebraic structure and the
energy-reflection symmetry, we construct a daughter N-body Hamiltonian
presenting a deformation of the Calogero model. The features of this
Hamiltonian are (i) it reduces to a quadratic combination of the generators of
sl(N+1); (ii) the interaction potential contains two-body terms and interaction
with the force center at the origin; (iii) for quantized values of a certain
cohomology parameter n it is quasi-exactly solvable, the multiplicity of states
in the algebraic sector is (N+n)!/(N!n!); (iv) the energy-reflection symmetry
of the parent system is preserved.Comment: Latex, 12 page
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