Related papers: Planar Quantum Mechanics: an Intriguing Supersymme…
A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without…
We study the behaviour of a scalar field coupled to a noncommutative black hole which is described by a $\kappa$-cylinder Hopf algebra. We introduce a new class of realizations of this algebra which has a smooth limit as the deformation…
Superpotentials in ${\cal N}=2$ supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are…
Supersymmetry is an algebraic property of a quantum Hamiltonian that, by giving every boson a fermionic superpartner and vice versa, may underpin physics beyond the Standard Model. Fractional bosonic and fermionic quasiparticles are…
We study the unitary matrix model with a topological term. We call the topological term the theta term. In the symmetric model there is the phase transition between the strong and weak coupling regime at $\lambda_{c}=2$. If the Wilson term…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
In supersymmetric quantum mechanics the emergence of a singularity may lead to the breakdown of isospectrality between partner potentials. One of the regularization recipes is based on a topologically nontrivial, multisheeted complex…
We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by…
We deal with the Hamiltonian hierarchy problem of the Hulth\'{e}n potential within the frame of the supersymmetric quantum mechanics and find that the associated superymmetric partner potentials simulate the effect of the centrifugal…
We discuss two distinct aspects in supersymmetric quantum mechanics. First, we introduce a new class of operators A and $\bar{A}$ in terms of anticommutators between the momentum operator and N+1 arbitrary superpotentials. We show that…
The basic ideas in the theory of quantum mechanics on phase space are illustrated through an introduction of generalities, which seem to underlie most if not all such formulations and follow with examples taken primarily from kinematical…
In this project, we will develop the foundations of quantum mechanics using the methods of supersymmetry. We will discuss the use of the superpotential to derive the supersymmetric partner of a potential in one dimension, and explore…
The general features of the degeneracy structure of ($p=2$) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric…
The Snyder model is an example of noncommutative spacetime admitting a fundamental length scale $\beta$ and invariant under Lorentz transformations, that can be interpreted as a realization of the doubly special relativity axioms. Here, we…
A quantum mechanical model that realizes the $ \mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features with the well-known Witten model and is…
Planar supersymmetric quantum mechanical systems with separable spectral problem in curvilinear coordinates are analyzed in full generality. We explicitly construct the supersymmetric extension of the Euler/Pauli Hamiltonian describing the…
We propose a bosonic quantum breakdown Hubbard model, which generalizes the Bose-Hubbard model by adding an asymmetric breakdown interaction turning one boson into two between adjacent sites. When the normal hopping is zero, this model has…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e.…
Supersymmetric quantum mechanical models are computed by the Path integral approach. In the $\beta\rightarrow0$ limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of…