Related papers: Two-point function for the Maxwell field in flat R…
We propose a general approach to defining a contractive-like multivalued mappings $F$ which avoids any use of the Hausdorff distance between the sets $F(x)$ and $F(y)$. Various fixed point theorems are proved under a two-parameter control…
We study the two-point functions of a general class of random-length random walks on finite boxes in $\ZZ^d$ with $d\ge3$, and provide precise asymptotics for their behaviour. We show that the finite-box two-point function is asymptotic to…
A flat Fiedmann-Robertson-Walker (FRW) multi-scalar field cosmology is studied with a particular potential of the form $ \rm V(\phi,\sigma)=V_0 e^{-\lambda_1 \phi-\lambda_2 \sigma}$, which emerges as a relation between the time derivatives…
Free Maxwell theory on general four-manifolds may, under certain conditions on the background geometry, exhibit holomorphic factorization in its partition function. We show that when this occurs, new discrete symmetries emerge at orbifold…
Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a…
Local and non-local properties of Hawking radiation in the presence of short distance dispersion are computed using connection formulae. The robustness of the spectrum and that of the two-point function are explained by showing that the…
We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
The aim of this paper is to prove the existence of Hadamard states for the Maxwell equations on any globally hyperbolic spacetime. This will be achieved by introducing a new gauge fixing condition, the Cauchy radiation gauge, that will…
Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the region between two infinite parallel…
The Wightman function i.e. vacuum two-point function, for a massless free scalar field in Fock quantization is inversely proportional to the invariant distance squared between the corresponding spacetime points. Naturally it diverges when…
We holographically calculate two-point functions in the pseudo-conformal universe, an early universe alternative to inflation. The pseudo-conformal universe can be modeled as a defect conformal field theory, where the reheating surface is a…
By iterative techniques,we present two fixed point theorems, whose modular formulations are relatively close to the Banach's fixed point theorem in the normed spaces.The first result concerns the fixed point of the strongly contraction…
This paper studies magnetic line defects in the Wilson-Fisher $O(N)$ model. A powerful method to probe the system is to consider mixed two-point functions of the order parameter and the energy operator in the presence of the defect. A…
In this paper, the notion of $\mathcal{W}$-property for subsets of $X\times X^{\lozenge}$ is introduced and investigated, where $X$ is an Hadamard space and $X^{\lozenge}$ is its linear dual space. It is shown that an Hadamard space $X$ is…
Recent work in the literature has found a suppression or, instead, an enhancement of the Cosmic Microwave Background power spectrum in quantum gravity, although the effect is too small to be observed, in both cases. The present paper…
Two-point correlation functions are ubiquitous tools of modern cosmology, appearing in disparate topics ranging from cosmological inflation to late-time astrophysics. When the background spacetime is maximally symmetric, invariance…
We give a rigorous derivation of the general-relativistic formula for the two-way Doppler tracking of a spacecraft in Friedmann-Lemaitre-Robertson-Walker and in McVittie spacetimes. The leading order corrections of the so-determined…
This paper aims to show that making use of Newton's view on equations of motion of a physical system and of the Maxwell stress tensor we come to a natural nonlinearization of Maxwell equations in vacuum making use only of nonrelativistic…
Following Kottler, \'E.Cartan, and van Dantzig, we formulate the Maxwell equations in a metric independent form in terms of the field strength $F=(E,B)$ and the excitation $H=({\cal D}, {\cal H})$. We assume a linear constitutive law…