Related papers: An explicit Koppelman formula for $dd^c$ and Green…
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
The direct method of construction of local conservation laws of partial differential equations (PDE) is a systematic method applicable to a wide class of PDE systems [Anco S. and Bluman G., Direct construction method for conservation laws…
Recently a definition for a Lorentz invariant operator approximating the d'Alembertian in d-dimensional causal set space-times has been proposed. This operator contains several dimension-dependent constants which have been determined for…
Given a linear recurrence of the form $c_n=a_1c_{n-1}+\cdots+a_j c_{n-j}$, it is well-known that $c_n=\sum_{r}p_r(n)r^n$, where the sum is taken over the set of characteristic roots and each $p_r(n)$ is some polynomial. We give a closed…
The ellipsoidal superpotential of the complex projective plane can be interpreted as a count of rigid rational plane curves of a given degree with one prescribed cusp singularity. In this note we present a closed formula for these counts as…
In this paper I discuss a formulation of relativistic few-particle scattering theory where the dynamical input is a collection of reflection-positive Euclidean covariant Green functions. This formulation of relativistic quantum mechanics…
The reduction formulas for Dirac fermions are derived, using the exact solutions of free Dirac equation on de Sitter spacetime. In the framework of the perturbation theory one studies the Green functions and derive the scatering amplitude…
We derive a formula connecting in any dimension the Green function on the D+1 dimensional Euclidean Rindler space and the one for a minimally coupled scalar field with a mass m in the D dimensional hyperbolic space. The relation takes a…
The polarization operator (tensor) for planar charged fermions in constant uniform magnetic field is calculated in the one-loop approximation of the 2+1 dimensional quantum electrodynamics (QED$_{2+1}$) with a nonzero fermion density. We…
We present a theoretical method to calculate Delbr\"uck scattering amplitudes. Our formalism is based on the exact analytical Dirac-Coulomb Green's function and, therefore, accounts for the interaction of the virtual electron-positron pair…
In this note, we derive an elementary version of the coarea formula by considering the mass of a solid body with density $g (x)$. Then we present an rigorous proof using the changing variable formula. To this end we construct the…
The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…
In formal scattering theory, Green functions are obtained as solutions of a distributional equation. In this paper, we use the Sturm-Liouville theory to compute Green functions within a rigorous mathematical theory. We shall show that both…
We argue that the process of constructing the quantum mechanical current of the Pauli equation by copying the line of arguments used in the spin-0 case, i.e. the Schr\"{o}dinger equation, is ambiguous. We show that a non-relativistic…
Exact analytic solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
We present general formulae to compute Wilson line correlators with the Color Glass Condensate described by the McLerran-Venugopalan model. We explicitly construct a complete and non-orthogonal set of color-singlet bases and write matrix…
We establish compactness estimates for $\bar{\partial}_{M}$ on a compact pseudoconvex CR-submanifold $M$ of $\mathbb{C}^{n}$ of hypersurface type that satisfies the (analogue of the) geometric sufficient conditions for compactness of the…
In this paper we show some exact solutions for the Caudrey-Dodd-Gibbon equation (CDG equation). These solutions are obtained via \circledR \emph{Mathematica} 6.0 by the projective Riccati equation method.
We introduce a division formula on a possibly singular projective subvariety $X$ of complex projective space $\Pk^N$, which, e.g., provides explicit representations of solutions to various polynomial division problems on the affine part of…
Directed spaces are natural topological extensions of dcpos in domain theory and form a cartesian closed category. We will show that the D-completion of free algebras over a Scott space $\Sigma L$, on the context of directed spaces, are…