Related papers: Hidden symmetries and nonlinear (super)algebras
Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
It is shown that for N=2 supersymmetry a hidden symmetry arises from the hybrid structure of a quartic algebra. The implications for invariant Lagrangians and multiplets are explored.
The well known relation between extended supersymmetry and complex geometry in the non-linear sigma-models is reviewed, and some recent developments related to the introduction of the non-anti-commutativity, in the context of the…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
We show that some simple well studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Poschl-Teller…
A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy,…
The aim of this paper is to study symmetries of linearly singular differential equations, namely, equations that can not be written in normal form because the derivatives are multiplied by a singular linear operator. The concept of…
The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
A description of the motion in noninertial reference frames by means of the inclusion of high time derivatives is studied. Incompleteness of the description of physical reality is a problem of any theory, both in quantum mechanics and…
The additional hidden symmetry of the Coulomb-Kepler problem is reviewed in classical as well as in quantum mechanics. The main purpose is to elucidate the role of this kind of symmetries in the reduction of physical problems, to show…
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…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…
For some non-linear field theories which allow for soliton solutions, submodels with infinitely many conservation laws can be defined. Here we investigate the symmetries of the submodels, where in some cases we find a symmetry enhancement…
Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed ("apparent") or concealed by the perceived symmetry…