Economic analysis

Abstract

We emphasize intertwining relations as a universal tool in constructing onedimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly solvable operators with invariant subspaces of monomials. We show that the simplest case of generalized intertwining relations allows to naturally relate quasi-exactly solvable operators with two invariant monomial subspaces to a nonlinear parasupersymmetry of second order. Quantum-mechanical systems with linear and nonlinear supersymmetry are discussed from the viewpoint of quasi-exact solvability. We construct such a general system with a cubic supersymmetry and argue that quantum-mechanical systems with nonlinear supersymmetry of fourth order and higher are generally not quasi-exactly solvable. Besides, we construct two examples of quasi-exactly solvable operators with invariant subspaces which cannot be reduced to monomial spaces. *

On Manifolds Admitting the Consistent Lagrangian Formulation for Higher Spin Fields

“…The essence of the problem is that any naive (e.g. minimal) including the interaction to free higher spin field Lagrangian violates consistency of the equations of motion (see the various aspects of the inconsistency in [2,3,4]). One of the partial aspects of the generic problem is a Lagrangian formulation for higher spin fields coupled to external background.…”

“…Some approaches to such Lagrangians are given in refs. [3,4]. Also, it would be interesting to study the consistency conditions for for recently formulated conformal higher spin fields [16] if to couple them to external fields.…”