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We study a family of modules over Kac-Moody algebras realized in multi-valued functions on a flag manifold and find integral representations for intertwining operators acting on these modules. These intertwiners are related to some…
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
Green-hyperbolic operators are linear differential operators acting on sections of a vector bundle over a Lorentzian manifold which possess advanced and retarded Green's operators. The most prominent examples are wave operators and…
Ladder operators for the hyperbolic Rosen-Morse (RMII) potential are realized using the shape invariance property appearing, in particular, using supersymmetric quantum mechanics. The extension of the ladder operators to a specific class of…
Three questions about the intertwining operators for the generalized principal series on a symmetric R-space are solved : description of the functional kernel, both in the compact and the non-compact picture, domain of convergence,…
We consider a one-dimensional optical lattice of three-dimensional Harmonic Oscillators which are loaded with neutral fermionic atoms trapped into two hyperfine states. By means of a standard variational coherent-state procedure, we derive…
We present a Melnikov type approach for establishing transversal intersections of stable/unstable manifolds of perturbed normally hyperbolic invariant manifolds (NHIMs). The method is based on a new geometric proof of the normally…
We construct a parametrix of a resolvent of elliptic differential operators acting on half-densities on manifolds with ends. The construction is carried out by introducing suitable pseudodifferential operators compatible with the end…
The anomaly of non-invertible higher-form symmetries is determined by the braiding of topological operators implementing them. In this paper, we study a method to classify braidings on topological line and surface operators by leveraging…
We complete the classification of ruled real hypersurfaces with shape operator of constant norm in nonflat complex space forms by showing the existence of a unique inhomogeneous example in the complex hyperbolic space.
We solve the problem of describing all nonlocal Hamiltonian operators of hydrodynamic type with flat metrics. This problem is also equivalent to the description of all flat submanifolds with flat normal bundle in a pseudo-Euclidean space.…
A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…
A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining inner product of the physical…
We prove a result on the structure of finite proper holomorphic mappings between complex manifolds that are products of hyperbolic Riemann surfaces. While an important special case of our result follows from the ideas developed by Remmert…
In this paper the path integral technique is applied to the quantum motion on the Hermitian hyperbolic space HH(2). The Schr\"odinger equation on this space separates in 12 coordinate systems which are closely related to the coordinate…
A physical requirement on the Hamiltonian operator in quantum mechanics is that it must generate real energy spectrum and unitary time evolution. While the Hamiltonians are Dirac Hermitian in conventional quantum mechanics, they observe…
When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials…