Related papers: A dynamical symmetry for supermembranes
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose…
Supersymmetric nonlinear sigma models have target spaces that carry interesting geometry. The geometry is richer the more supersymmetries the model has. The study of models with two dimensional world sheets is particularly rewarding since…
The kinematical and dynamical symmetries of equations describing the time evolution of quantum systems like the supersymmetric harmonic oscillator in one space dimension and the interaction of a non-relativistic spin one-half particle in a…
We study the kinematics and dynamics of a highly compliant membrane disk placed head-on in a uniform flow. With increasing flow velocity, the membrane deforms nonlinearly into increasingly parachute-like shapes. These aerodynamically…
In this contribution the symmetry properties of the interacting boson model of Arima and Iachello are reviewed. While the concept of a dynamical symmetry is by now a familiar one, this is not necessarily so for the extended notions of…
Utilizing techniques suggested by the recently obtained construction of off-shell spinning particles, we propose the arbitrary $N$-extension of supersymmetry for the KdV system. It is further suggested that the ${\aleph}_0$ extension for…
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…
We investigate $N$-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer $n$, $N=2n+1$ supercharges are explicitly constructed in terms of discrete transformations, and a class of…
In this work we study the recently introduced octonionic duality for membranes. Restricting the self - duality equations to seven space dimensions, we provide various forms for them which exhibit the symmetries of the octonionic and…
Growth processes in many living organisms create thin, soft materials with an intrinsically hyperbolic geometry. These objects support novel types of mesoscopic defects - discontinuity lines for the second derivative and branch points -…
In this paper, we achieve some interesting results in the way to make sense how superparticles interact together and to ordinary particles by means of putting aside the dimensional constraints. This is the first step in the process of…
We present an efficient method to understand the p-brane dynamics in a unified framework. For this purpose, we reformulate the action for super p-branes in the form appropriate to incorporate the pointlike (parton) structure of higher…
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a…
We consider higher symmetries and operator symmetries of linear partial differential equations. The higher symmetries form a Lie algebra, and operator ones form an associative algebra. The relationship between these symmetries is…
We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited,…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
We review the subject of spontaneous supersymmetry breaking. First we consider supersymmetry breaking in a semiclassical theory. We illustrate it with several examples, demonstrating different phenomena, including metastable supersymmetry…
There is constructed and considered the extension of classical Diriclet operator corresponding to uniformly log-concave measure in the space of symmetric differential forms. Sufficient conditions for its essential self-adjointness in…
Mechanical metamaterials leverage geometric design to achieve unconventional properties, such as high strength at low density, efficient wave guiding, and complex shape morphing. The ability to control shape changes builds on the complex…
This study is an extented analogue to conformal geometry of the paper given by [14]. Also, the geometric and physical results related to bi-para-conformal-dynamical systems are also presented.