Related papers: Noninteger flux - why it does not work
We prove that the Neumann, Dirichlet and regularity problems for divergence form elliptic equations in the half space are well posed in $L_2$ for small complex $L_\infty$ perturbations of a coefficient matrix which is either real symmetric,…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
We consider an elliptic self-adjoint first order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of our operator is…
In this paper, we consider the eigenvalue problem of Dirac operator on a compact Riemannian manifold isometrically immersed into Euclidean space and derive some extrinsic estimates for the sum of arbitrary consecutive $n$ eigenvalues of the…
We extend naturally the spectral triple which define noncommutative geometry (NCG) in order to incorporate supersymmetry and obtain supersymmetric Dirac operator D_M which acts on Minkowskian manifold. Inversely, we can consider the…
We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…
We summarize a recent work on the subject title. The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions…
In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman…
We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at…
It is of general theoretical interest to investigate the properties of superluminal matter wave equations for spin one-half particles. One can either enforce superluminal propagation by an explicit substitution of the real mass term for an…
The Invariant Subspace Problem (ISP) for Hilbert spaces asks if every bounded linear operator has a non-trivial closed invariant subspace. Due to the existence of universal operators (in the sense of Rota) the ISP can be solved by proving…
A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional…
We show that the Dirac operator on a spin manifold does not admit $L^2$ eigenspinors provided the metric has a certain asymptotic behaviour and is a warped product near infinity. These conditions on the metric are fulfilled in particular if…
We study $4$-dimensional $SU(N)\times U(1)$ gauge theories with a single massless Dirac fermion in the $2$-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible $0$-form $\widetilde {\mathbb…
multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…
A bounded linear operator T on Hilbert space is subspace-hypercyclic for a subspace M if there exists a vector whose orbit under T intersects the subspace in a relatively dense set. We construct examples to show that subspace-hypercyclicity…
In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on…
We consider half-line Dirac operators with operator data of Wigner-von Neumann type. If the data is a finite linear combination of Wigner-von Neumann functions, we show absence of singular continuous spectrum and provide an explicit set…
The q-deformed fuzzy sphere $S_{qF}^2(N)$ is the algebra of $(N+1)\times(N+1)$ dim. matrices, covariant with respect to the adjoint action of $\uq$ and in the limit $q\to 1$, it reduces to the fuzzy sphere $S_{F}^2(N)$. We construct the…
We present a summary of: 1) the non-uniqueness problem of the Hamiltonian and energy operators associated, in any given coordinate system, with the generally-covariant Dirac equation; 2) two different ways to restrict the gauge freedom so…