Related papers: CM Values of Higher Green's Functions
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…
The gauge invariant quark Green's function, defined with a path-ordered phase factor along a straight line, is studied in two-dimensional QCD in the large-N_c limit by means of an exact integrodifferential equation. It is found to be…
We construct the explicit Euclidean scalar Green function associated with a massless field in a higher dimensional global monopole spacetime, i.e., a $(1+d)$-spacetime with $d\geq3$ which presents a solid angle deficit. Our result is…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
This paper is a sequel to our previous work, where we proved the ``modularity theorem'' for algebraic Witt vectors over imaginary quadratic fields. This theorem states that, in the case of imaginary quadratic fields $K$, the algebraic Witt…
We develop Green's function formalism to describe continuous multi-layered quasi-one-dimensional setups described by piece-wise constant single-particle Hamiltonians. The Hamiltonians of the individual layers are assumed to be quadratic…
Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing…
We study the single-band Hubbard model under the action of an external magnetic field using the cumulant Green's functions method (CGFM). The starting point of the method is to diagonalize a cluster containing N correlated sites (seed) and…
A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations…
Under a largeness assumption on the size of the residue field, we give an explicit description of the positive-depth Deligne--Lusztig induction of unramified elliptic pairs $(T,\theta)$. When $\theta$ is regular, we show that positive-depth…
One of the landmarks of the modern theory of partial differential equations is the Malgrange- Ehrenpreis theorem that states that every non-zero linear partial differential operator with constant coefficients has a Green function (alias…
We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a…
The purpose of this paper is to find optimal estimates for the Green function of a half-space of {\it the relativistic $\alpha$-stable process} with parameter $m$ on $\Rd$ space. This process has an infinitesimal generator of the form…
The Green functions were first introduced by Green to compute the character table of GLn(q) in 1955. They were later generalized by Deligne and Lusztig for an arbitrary finite group of Lie type G(q) using l-adic cohomological methods…
We revisit the classical phenomenon of duality between random integer-valued height functions with positive definite potentials and abelian spin models with O(2) symmetry. We use it to derive new results in quite high generality including:…
We prove a higher weight general Gross--Zagier formula for CM cycles on Kuga--Sato varieties over modular curves of arbitrary levels. To formulate and prove this result, we prove several results on the modularity of CM cycles, in the sense…