Related papers: Shape Invariant Potentials in Higher Dimensions
Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…
The issue of field redefinition invariance of path integrals in quantum field theory is reexamined. A ``paradox'' is presented involving the reduction to an effective quantum-mechanical theory of a $(d+1)$-dimensional free scalar field in a…
In its most general form, the recognition problem in Riemannian geometry asks for the identification of an unknown Riemannian manifold via measurements of metric invariants on the manifold. We introduce a new infinite sequence of…
String-localized quantum field theory allows renormalizable couplings involving massive vector bosons, without invoking negative-norm states and compensating ghosts. We analyze the most general coupling of a massive vector boson to a scalar…
Recently, Quesne on the one side and on the other side Bougie, Gangopadhyaya and Mallow, have discovered new translational shape invariant potentials not present in previous classifications. By using ordinary B\"acklund--Darboux…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
It is shown that for a class of position dependent mass Schroedinger equation the shape invariance condition is equivalent to a potential symmetry algebra. Explicit realization of such algebras have been obtained for some shape invariant…
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in…
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…
We report on the recent results revealing the presence of geometric invariants in all the phenomena in which vacuum condensates appear and we show that Aharonov--Anandan phase can be used to provide the evidence of phenomena like Hawking…
The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
We suppose: (1) that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -Delta + vf(x) in one dimension is known for all values of the coupling v > 0; and (2) that the potential shape can be expressed in the form f(x)…
In shape analysis, the concept of shape spaces has always been vague, requiring a case-by-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes in a manifold. This notion…
Supersymmetry, shape invariance, exact solubility, and the factorization method are often studied together in the literature. At the dawn of these topics confusion was present in regards to their scope of applicability and the relation…
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,…
Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…