相关论文: On supersymmetries in nonrelativistic quantum mech…

A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…

Nonlinear SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. Possible multidimensional extensions of Nonlinear SUSY are described. The full classification of ladder-reducible and irreducible…

I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances.…

We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincar\'e group. For particular values of the parameters appearing in the lagrangian the model has a…

We introduce a smooth mapping of some discrete space-time symmetries into quasi-continuous ones. Such transformations are related with q-deformations of the dilations of the Euclidean space and with the non-commutative space. We work out…

We develop an algebraic approach to studying the spectral properties of the stationary Schr\"odinger equation in one dimension based on its high order conditional symmetries. This approach makes it possible to obtain in explicit form…

It is shown how nonlinear versions of quantum mechanics can be refolmulated in terms of a (linear) C*-algebraic theory. Then also their symmetries are described as automorphisms of the correspondong C*-algebra. The requirement of…

We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to…

First order integrals of motion for Schr\"odinger equations with position dependent masses are classified. Seventeen classes of such equations with non-equivalent symmetries are specified. They include integrable, superintegrable and…

The maximal algebra of symmetries of the free single-particle Schroedinger equation is determined and its relevance for the holographic duality in non-relativistic Fermi systems is investigated. This algebra of symmetries is an infinite…

A deformation of the canonical algebra for kinematical observables of the quantum field theory in Minkowski space-time has been considered under the condition of Lorentz invariance. A relativistic invariant algebra obtained depends on…

We classify $N{=}1$ $d=4$ kinematical and aristotelian Lie superalgebras with spatial isotropy, but not necessarily parity nor time-reversal invariance. Employing a quaternionic formalism which makes rotational covariance manifest and…

These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some…

The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to 10 dimensional. The…

Fractional supersymmetric quantum mechanics is developed from a generalized Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional supersymmetric dynamical systems are built in terms of the generators of this algebra.…

We describe the twisted space-time symmetries which imply the quantum Poincar\'{e} covariance of noncommutative Minkowski spaces, with constant, Lie algebraic and quadratic commutators. Further we present the relativistic and…

One examines the infinitely deep quantum cavity, also known as the quantum infinite square well, within the framework of the real Hilbert space. The solutions are considered in terms of complex wave functions, and also in terms of…

We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…

Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…

We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…