Related papers: The spectral function of a first order system

We consider a general second-order elliptic differential operator on a domain with a cylindrical end. We impose Dirichlet boundary conditions on the boundary with the exception of a small set, where we impose Neumann boundary conditions.…

A supersymmetric theory in two-dimensions has enough data to define a noncommutative space thus making it possible to use all the tools of noncommutative geometry. In particular, we apply this to the N=1 supersymmetric non-linear sigma…

This paper is devoted to mathematical and physical properties of the Dirac operator and spectral geometry. Spin-structures in Lorentzian and Riemannian manifolds, and the global theory of the Dirac operator, are first analyzed. Elliptic…

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…

A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal…

We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function. We calculate first two Gilkey-de Witt coefficients and make explicit calculations…

We initiate a systematic study of natural differential operators in Riemannian geometry whose leading symbols are not of Laplace type. In particular, we define a discrete leading symbol for such operators which may be computed pointwise, or…

Is considered the asymptotical behavior of spectral function $\rho(\lambda, \epsilon),\epsilon > 0$, of one family of self adjoint differential operators of second order, defined in space $L_2[0,+\infty)$ with potentials, depending on…

We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to…

We discuss the behaviour of the spectral density of the massless Dirac operator at the small eigenvalues and quark masses compatible with the restrictions imposed by the low energy theorems in QCD. Sum rule for its derivative over the quark…

We consider 1d-Dirac operator $\mathcal L_{P,U}$ acting in $\mathbb H=(L_2[0,\pi])^2$ \begin{gather*} \ell(\mathbf y) = B\mathbf y + P(x)\mathbf y,\qquad B = \begin{pmatrix}-i&0\\0&i\end{pmatrix},\\ P(x) = \begin{pmatrix}p_1(x)&p_2(x)\\…

We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar $\delta$-shell interaction of strength $\tau\in\mathbb{R}\setminus\{-2,0,2\}$ supported on a broken line…

We consider the self-adjoint operator $H=H_0+V$, where $H_0$ is the free semi-classical Dirac operator on $R^3$. We suppose that the smooth matrix-valued potential $V=O(<x>^{-\delta}), \delta>0,$ has an analytic continuation in a complex…

We study the pseudospectrum of a class of non-selfadjoint differential operators. Our work consists in a detailed study of the microlocal properties, which rule the spectral stability or instability phenomena appearing under small…

We consider the self-adjoint fourth-order operator with real $1$-periodic coefficients on the unit interval. The spectrum of this operator is discrete. We determine the high energy asymptotics for its eigenvalues.

We consider the operator $H={d^4dt^4}+{ddt}p{ddt}+q$ with 1-periodic coefficients on the real line. The spectrum of $H$ is absolutely continuous and consists of intervals separated by gaps. We describe the spectrum of this operator in terms…

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…

We study sub-Dirac operators that are associated with left-invariant bracket-generating sub-Riemannian structures on compact quotients of nilpotent semi-direct products $G=\mathbb{R}^n\rtimes_A\mathbb{R}$. We will prove that these operators…

We give an expression, in terms of boundary spectral functions, for the spectral asymmetry of the Euclidean Dirac operator in two dimensions, when its domain is determined by local boundary conditions, and the manifold is of product type.…

We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar $\delta$-interactions of constant strengths supported on a smooth closed curve. For any combination of the coupling constants a…