Related papers: Time varying axially symmetric vector random field…
We show how gauge-invariant cosmological perturbations may be constructed by an unambiguous choice of hypersurface-orthogonal time-like vector field (i.e., time-slicing). This may be defined either in terms of the metric quantities such as…
By directly probing the initial conditions of our universe, cosmological surveys offer us a unique observational handle on quantum field theory in curved spacetime with dynamical gravity and might even allow us to glean information about a…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
Modern datasets are often in the form of matrices or arrays,potentially having correlations along each set of data indices. For example, data involving repeated measurements of several variables over time may exhibit temporal correlation as…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…
This article presents an overview of a theory for performing temporal smoothing on temporal signals in such a way that: (i) temporally smoothed signals at coarser temporal scales are guaranteed to constitute simplifications of corresponding…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
In this note, we provide a important considerations of a familiar topic: the gradient of a vector field. The gradient of a vector field is a common quantity represented in continuum mechanics. However, even for Cartesian coordinate systems,…
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…
Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by…
We develop the quantum field theory of fermion mixing in curved spacetime and discuss the role of unitarily inequivalent representations in the particle interpretation of the theory. We derive general oscillation formulae and apply them to…
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
In a general linear model, this paper derives a necessary and sufficient condition under which two general ridge estimators coincide with each other. The condition is given as a structure of the dispersion matrix of the error term. Since…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
The paper construct a suitable generalized metrical multi-time Lagrange geometrical model for both gravitational and electromagnetic fields, in a general setting. In this construction, the gravitational potentials are described by a…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
The question of whether unobserved short-wavelength modes of the gravitational field can induce decoherence in the long-wavelength modes (``the decoherence of spacetime'') is addressed using a scalar field toy model with some features of…
We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal…
The role of the time surface term in the ADM Hamiltonian formulation of general relativity is investigated. We show that the variable contained in the time surface term (the scale factor) plays the role of a time-like variable. The…
Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of minisuperspace models in the presence of scalar fields together with the inhomogeneous modes either of the gravitational or of the scalar fields.…