Related papers: Green equivalences in equivariant mathematics
Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from…
Based on the technique of derivation of a theory, presented in our recent paper, we investigate the properties of the derived quantum system. We show that the derived quantum system possesses the (nonanomalous) symmetries of the original…
Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SU_q(2), the Green function and the Kernel on the q-homogeneous space M=SU(2)_q/U(1) are derived. A path integration is formulated.…
We construct a map from the suspension $G$-spectrum $\Sigma_G^\infty M$ of a smooth compact $G$-manifold to the equivariant $A$-theory spectrum $A_G(M)$, and we show that its fiber is, on fixed points, a wedge of stable $h$-cobordism…
We introduce reflection functors on quiver schemes in the sense of Hausel--Wong--Wyss, generalizing those on quiver varieties. Also we construct some isomorphisms between quiver schemes whose underlying quivers are different.
The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's function solutions of nonlinear differential equations of higher…
This report provides Green's functions (classical propagators) of gravitational fields appearing in general relativity. The existence of Green's function of the wave equation in curved space with an indefinite metric is ensured owing to the…
We study quantization of a gauge analogon of the Grosse-Wulkenhaar model: we find divergent one-loop contributions to the 1-point and 2-point Green functions. We obtain that five counterterms are necessary for renormalization and that all…
We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness,…
This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem…
An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous…
We establish existence and various estimates of fundamental matrices and Green's matrices for divergence form, second order strongly parabolic systems in arbitrary cylindrical domains under the assumption that solutions of the systems…
We give an alternative method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method using tools from invariant theory to establish formulae that take symmetries into account as a starting point.…
We study the one-dimensional Schr\"odinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite intervals. We also discuss the relation between our results and…
An expression for the Green function G(E;x_1,x_2) of the Schroedinger equation is obtained through the approximations of the path integral by n-fold multiple integrals. The approximations to Re{G(E;x,x)} on the real E-axis have peaks near…
Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem…
We propose a new method to compute the $C_{2^n}$-equivariant homotopy groups of the Eilenberg-Mac Lane spectrum $H\underline{\mathbb{Z}}$ as a $RO(C_{2^n})$-graded Green functor using the generalized Tate squares. As an example, we…
The aim of this work is to outline in some detail the use of combinatorial algebra in planar quantum field theory. Particular emphasis is given to the relations between the different types of planar Green's functions. The key object is a…
In this paper, the Green function theory of quantum many-particle systems recently presented is reworked within the framework of nonextensive statistical mechanics with a new normalized $q$-expectation values. This reformulation introduces…
Using Gegenbauer polynomials and the zonal harmonic functions we build an explicit representation formula for the Green function with Neumann boundary conditions in the annulus.