Related papers: Green's functions for magnetic Dirac operators and…
In this dissertation I establish that a broad class of Banach *-algebras of infinite integral operators, defined by the property that the kernels of the elements of the algebras possess subexponential off-diagonal decay, is inverse closed…
In this paper, we prove a generalization of Green's Hyperplane Restriction Theorem to the case of modules over the polynomial ring, providing in particular an upper bound for the Hilbert function of the general linear restriction of a…
We show existence, uniqueness and positivity for the Green's function of the operator $(\Delta_g + \alpha)^k$ in a closed Riemannian manifold $(M,g)$, of dimension $n>2k$, $k\in \mathbb{N}$, $k\geq 1$, with Laplace-Beltrami operator…
The zeta and eta-functions associated with massless and massive Dirac operators, in a D-dimensional (D odd or even) manifold without boundary, are rigorously constructed. Several mathematical subtleties involved in this process are…
Using a five dimensional (5D) warped model with two branes along the extra dimension, we study the Green's functions for gauge bosons with a mass gap $m_g = \rho/2$ and a continuum for $s > m_g^2$. We find that the Green's functions exhibit…
We derive a cancellation property satisfied by the derivatives of the Green's functions for the Laplace operator corresponding to Dirichlet and Neumann boundary conditions on bounded sets in $\R^n$. The main result is derived in a broader,…
In this paper we give a definition of (centric) Mackey functor over a fusion system which generalizes the notion of Mackey functor over a group. In this context we prove that, given some conditions on a related ring, the centric Burnside…
We consider magnetic Schr\"odinger operators describing a quantum Hall effect setup both in the plane and in the half-plane. First, we study the structure and smoothness of the operator range of various powers of the half-plane resolvent.…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is discussed. For weak magnetic fields, the approximate energy values are obtained by semiclassical method. In the case with strong…
We summarize the work done in connecting Green's functions in a different classes of gauges and its applications to the problems in the axial gauges.The procedure adopted uses finite field-dependent BRS [FFBRS] transformations to connect…
Inspired by the recent proposed Legendre orthogonal polynomial representation of imaginary-time Green's functions, we develop an alternate representation for the Green's functions of quantum impurity models and combine it with the…
We consider the semi-classical Dirac operator coupled to a magnetic potential on a large class of manifolds including all metric contact manifolds. We prove a sharp local Weyl law and a bound on its eta invariant. In the absence of a…
We introduce a new equation we dubbed the modular Dirac equation to see and reconstruct a spin 1/2 particle at the center of a nearly $AdS_2$ spacetime in the entanglement wedge reconstruction paradigm and we study hidden symmetries of this…
In this paper we continue our investigation of the potential theory of Markov processes with jump kernels decaying at the boundary. To be more precise, we consider processes in ${\mathbb R}^d_+$ with jump kernels of the form ${\mathcal…
We develop novel first-kind boundary integral equations for Euclidean Dirac operators in 3D Lipschitz domains comprising square-integrable potentials and involving only weakly singular kernels. Generalized Garding inequalities are derived…
Recent applications of large network models to machine learning, and to neural network suggest a need for a systematic study of the general correspondence, (i) discrete vs (ii) continuous. Even if the starting point is (i), limit…
Let $M$ be an oriented even-dimensional Riemannian manifold on which a discrete group $\Gamma$ of orientation-preserving isometries acts freely, so that the quotient $X=M/\Gamma$ is compact. We prove a vanishing theorem for a half-kernel of…
Recent work on the quantization of Maxwell theory has used a non-covariant class of gauge-averaging functionals which include explicitly the effects of the extrinsic-curvature tensor of the boundary, or covariant gauges which, unlike the…
The paper is concerned with the completeness property of root functions of the $2\times 2$ Dirac operator with summable complex-valued potential and non-regular boundary conditions. Sufficient conditions for the completeness of the root…