Principle Of Covariance Research Articles

Sterile neutrinos existence suggested from LCT covariance

Sterile neutrinos are known to be hypothetical neutrinos which do not interact via the fundamental interactions described within the Standard Model of Particles Physics i.e. electroweak and strong interactions. They are expected to be important for the understanding of the physics beyond the current Standard Model. In the present work, it is shown that the existence of these particles can be suggested from covariance principle using a covariance group formed by Linear Canonical Transformations (LCTs) associated to a pentadimensional pseudo-Euclidian space. It is established that a spin representation of the LCT group gives a particle classification, applicable to the three families of leptons and quarks, which leads to the prediction of the existence of three sterile neutrinos and their antiparticles.

Covariance Principle for Capital Allocation: A Time-Varying Approach

The covariance allocation principle is one of the most widely used capital allocation principles in practice. Risks change over time, so capital risk allocations should be time-dependent. In this paper, we propose a dynamic covariance capital allocation principle based on the variance-covariance of risks that change over time. The conditional correlation of risks is modeled by means of a dynamic conditional correlation (DCC) model. Unlike the static approach, we show that in our dynamic capital allocation setting, the distribution of risk capital allocations can be estimated, and the expected future allocations of capital can be predicted, providing a deeper understanding of the stochastic multivariate behavior of risks. The methodology presented in the paper is illustrated with an example involving the investment risk in a stock portfolio.

Covariant theory of light in a dispersive medium

The relativistic theory of the time- and position-dependent energy and momentum densities of light in glasses and other low-loss dispersive media, where different wavelengths of light propagate at different phase velocities, has remained a largely unsolved challenge until now. This is astonishing in view of the excellent theoretical understanding of Maxwell's equations and the abundant experimental measurements of optical phenomena in dispersive media. The challenge is related to the complexity of the interference patterns of partial waves and to the coupling of the field and medium dynamics by the optical force. In this work, we use the mass-polariton theory of light [Phys. Rev. A 96, 063834 (2017)] to derive the stress-energy-momentum (SEM) tensors of the field and the dispersive medium. Our starting point, the fundamental local conservation laws of energy and momentum, is close to that of a recent theoretical work on light in dispersive media by Philbin [Phys. Rev. A 83, 013823 (2011)], which however, excludes the power-conversion and force density source terms describing the coupling between the field and the medium. In the general inertial frame, we present the SEM tensors in terms of Lorentz scalars, four-vectors, and field tensors that reflect in a transparent way the Lorentz covariance of the theory. The SEM tensors of the field and the medium are symmetric, form-invariant, and in full accordance with the covariance principle of the special theory of relativity. The SEM tensor of the coupled field-medium state of light also has zero four-divergence. Therefore, light in a dispersive medium has well-defined four-momentum and rest frame. The volume integrals of the total energy and momentum densities of light agree with the model of mass-polariton quasiparticles having a nonzero rest mass. The predictions of our work are directly accessible to experiments.

Path integrals for causal diamonds and the covariant entropy principle

We study causal diamonds in Minkowski, Schwarzschild, (anti) de Sitter, and Schwarzschild-de Sitter spacetimes using Euclidean methods. The null boundaries of causal diamonds are shown to map to isolated punctures in the Euclidean continuation of the parent manifold. Boundary terms around these punctures decrease the Euclidean action by $A_\diamond/4$, where $A_\diamond$ is the area of the holographic screen around the diamond. We identify these boundary contributions with the maximal entropy of gravitational degrees of freedom associated with the diamond.

Analytical Solution to FRW Metric with Variable Speed of Light

<p>According to the principle of general covariance, the laws of physics are the same in all reference frames. The controversial theory of the Varying Speed of Light (VSL) contradicts the principle of general covariance. Fortunately the VLS theory explains some crucial issues in cosmology such as Lorentz variance, biometric theories, locally Lorentz variance, cosmological constant problem, horizon<em> </em>and flatness<em> </em>problems. Also, recent astronomical observations from quasar show that the fine structural constant depends on redshift and therefore, varies with cosmological time. In other to harness this fascinating and published knowledge, two models where used in this work. 1. Cosmology with variables c; here the Friedmann-Robertson-Walker (FRW) is used in the Einstein field equation with variable c and Λ terms to obtain the scale factor, which shows the continuous exponential expansion of the universe. 2. Variation of the speed of light as a function of the scale factor of the universe; here we obtained: a good approximation to estimate the current age of the universe. The scale factor of the universe depends its content given by the equation of state parameter ω. We obtained the deceleration parameter in terms of the Hubble parameter. We arrived at a conclusion that the universe was decelerating at ω = 1, accelerating at ω = 1/3 and the Hubble parameter diverges at the beginning and end of the universe.</p>

Linear Canonical Transformations in relativistic quantum physics

Linear Canonical Transformations (LCTs) are known in signal processing and optics as the generalization of certain useful integral transforms. In quantum theory, they can be identified as the linear transformations which keep invariant the canonical commutation relations characterizing the coordinates and momenta operators. In this work, the possibility of considering LCTs to be the elements of a symmetry group for relativistic quantum physics is studied using the principle of covariance. It is established that Lorentz transformations and multidimensional Fourier transforms are particular cases of LCTs and some of the main symmetry groups currently considered in relativistic theories can be obtained from the contractions of LCTs groups. It is also shown that a link can be established between a spinorial representation of LCTs and some properties of elementary fermions. This link leads to a classification which suggests the existence of sterile neutrinos and the possibility of describing a generation of fermions with a single field. Some possible applications of the obtained results are discussed. These results may, in particular, help in the establishment of a unified theory of fundamental interactions. Intuitively, LCTs correspond to linear combinations of energy-momentum and spacetime compatible with the principle of covariance.

A Pedagogical Model of General Covariance Coupling Electrodynamics and Gravitation

In his 1951 model of the effects of a star’s radiation on its gravitation, P.C. Vaidya used radiation fields of flat spacetime. Wondering why Vaidya did not include the effects of gravitation on electrodynamics, we apply the principle of general covariance to gravitation and radiation. Others have addressed this problem with numerical methods, but, like Vaidya, we seek an analytic solution. Along the way, we see how prescient was Vaidya’s choice in modeling the radiation. Pursued originally as a pedagogical exercise with undergraduate physicists, our results compare favorably to similar models, and illustrate general relativity theorems. Given recent interest in teaching general relativity to undergraduates, a system that couples gravitation and electrodynamics and is solvable with elementary integrations may hold pedagogical interest.

The Principle of Covariance and the Hamiltonian Formulation of General Relativity.

The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the existence of a novel variational formulation in which the class of variations remains unconstrained. As a second step, the conditions of validity of the non-manifestly covariant ADM variational theory are questioned. The main result concerns the proof of its intrinsic non-Hamiltonian character and the failure of this approach in providing a symplectic structure of space-time. In contrast, it is demonstrated that a solution reconciling the physical requirements of covariance and manifest covariance of variational theory with the existence of a classical Hamiltonian structure for the gravitational field can be reached in the framework of synchronous variational principles. Both path-integral and volume-integral realizations of the Hamilton variational principle are explicitly determined and the corresponding physical interpretations are pointed out.

Spatial Covariant Management of Thermodynamics Contributes to Protein Fold Function Through Quality Assurance

Abstract Although the impact of genome variation on the thermodynamic properties of the protein fold has been studied in vitro, it remains a challenge to assign these relationships across the entire polypeptide sequence in vivo. Using the Gaussian process regression-based principle of Spatial CoVariance (SCV), we globally assign on a residue-by-residue the biological thermodynamic properties contributing to the functional fold in the cell using CFTR as an example. We demonstrate the existence of a thermodynamically sensitive region of the CFTR fold involving the interface between NBD1 and ICL4 that contributes to the endoplasmic reticulum (ER) export. At the cell surface a new set of residues contribute uniquely to the management of channel function. These results support a general 'quality assurance' (QA) view of global protein fold management as an SCV principle describing the differential pre- and post-ER residue interactions contributing to compartmentalization of the energetics of the protein fold for function.

A dissertation on General Covariance and its application in particle physics

In this paper, we provide a concise overview on the principle of General Covariance, one of the fundamental cornerstones of Einstein’s General Relativity. We retrace all the steps that led to the final settlement of a generally covariant theory of gravitation, dwelling specifically on the significance of the well-known “hole argument”. In addition, we discuss about the importance of General Covariance in connection with some recent claims in literature revolving around particle physics. In particular, we summarize the results associated with the decay of accelerated protons.

Symplectic group methods and the Arthurs Kelly model of measurement in quantum mechanics

We study the use of methods based on the real symplectic groups Sp(2n,R) in the analysis of the Arthurs-Kelly model of proposed simultaneous measurements of position and momentum in quantum mechanics. Consistent with the fact that such measurements are in fact not possible, with arbitrary precision, we show that the observable consequences of the Arthurs-Kelly interaction term are contained in the symplectic transformation law connecting the system plus apparatus variance matrices at an initial and a final time. The individual variance matrices are made up of averages and spreads or uncertainties for single hermitian observables one at a time, which are quantum mechanically well defined. The consequences of the multimode symplectic covariant Uncertainty Principle in the Arthurs-Kelly context are examined.

Holographic Space-Time and Quantum Information

The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-'t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamond's holographic screen, measured in Planck units. The most convincing argument for this principle is Jacobson's derivation of Einstein's equations as the hydrodynamic expression of this entropy law. In that context, the null energy condition (NEC) is seen to be the analog of the local law of entropy increase. The quantum version of Einstein's relativity principle is a set of constraints on the mutual quantum information shared by causal diamonds along different time-like trajectories. The implementation of this constraint for trajectories in relative motion is the greatest unsolved problem in HST. The other key feature of HST is its claim that, the degrees of freedom localized in the bulk of a diamond are constrained states of variables defined on the holographic screen. This principle gives a simple explanation of otherwise puzzling features of BH entropy formulae, and resolves the firewall problem for black holes in Minkowski space. It motivates a covariant version of the CKN\cite{ckn} bound on the regime of validity of quantum field theory (QFT) and a detailed picture of the way in which QFT emerges as an approximation to the exact theory.

Investigation on the Use of a Spacetime Formalism for Modeling and Numerical Simulations of Heat Conduction Phenomena

Abstract The question of frame-indifference of the thermomechanical models has to be addressed to deal correctly with the behavior of matter undergoing finite transformations. In this work, we propose to test a spacetime formalism to investigate the benefits of the covariance principle for application to covariant modeling and numerical simulations for finite transformations. Several models especially for heat conduction are proposed following this framework and next compared to existing models. This article also investigates numerical simulations using the heat equation with two different thermal dissipative models for heat conduction, without thermomechanical couplings. The numerical comparison between the spacetime thermal models derived in this work and the corresponding Newtonian thermal models, which adds the time as a discretized variable, is also performed through an example to investigate their advantages and drawbacks.

The algebra of Wick polynomials of a scalar field on a Riemannian manifold

On a connected, oriented, smooth Riemannian manifold without boundary we consider a real scalar field whose dynamics is ruled by [Formula: see text], a second-order elliptic partial differential operator of Laplace type. Using the functional formalism and working within the framework of algebraic quantum field theory and of the principle of general local covariance, first we construct the algebra of locally covariant observables in terms of equivariant sections of a bundle of smooth, regular polynomial functionals over the affine space of the parametrices associated to [Formula: see text]. Subsequently, adapting to the case in hand a strategy first introduced by Hollands and Wald in a Lorentzian setting, we prove the existence of Wick powers of the underlying field, extending the procedure to smooth, local and polynomial functionals and discussing in the process the regularization ambiguities of such procedure. Subsequently we endow the space of Wick powers with an algebra structure, dubbed E-product, which plays in a Riemannian setting the same role of the time-ordered product for field theories on globally hyperbolic spacetimes. In particular, we prove the existence of the E-product and we discuss both its properties and the renormalization ambiguities in the underlying procedure. As the last step, we extend the whole analysis to observables admitting derivatives of the field configurations and we discuss the quantum Møller operator which is used to investigate interacting models at a perturbative level.

Leveraging Population Genomics for Individualized Correction of the Hallmarks of Alpha-1 Antitrypsin Deficiency.

Deep medicine is rapidly moving towards a high-definition approach for therapeutic management of the patient as an individual given the rapid progress of genome sequencing technologies and machine learning algorithms. While considered a monogenic disease, alpha-1 antitrypsin (AAT) deficiency (AATD) patients present with complex and variable phenotypes we refer to as the "hallmarks of AATD" that involve distinct molecular mechanisms in the liver, plasma and lung tissues, likely due to both coding and non-coding variation as well as genetic and environmental modifiers in different individuals. Herein, we briefly review the current therapeutic strategies for the management of AATD. To embrace genetic diversity in the management of AATD, we provide an overview of the disease phenotypes of AATD patients harboring different AAT variants. Linking genotypic diversity to phenotypic diversity illustrates the potential for sequence-specific regions of AAT protein fold design to play very different roles during nascent synthesis in the liver and/or function in post-liver plasma and lung environments. We illustrate how to manage diversity with recently developed machine learning (ML) approaches that bridge sequence-to-function-to-structure knowledge gaps based on the principle of spatial covariance (SCV). SCV relationships provide a deep understanding of the genotype to phenotype transformation initiated by AAT variation in the population to address the role of genetic and environmental modifiers in the individual. Embracing the complexity of AATD in the population is critical for risk management and therapeutic intervention to generate a high definition medicine approach for the patient.

CO2 balance on oil palm agrosystem in Sumatra, Indonesia

The high demand and advantage of palm oil as vegetable oil for food and cosmetic products, and more recently for biofuels have led to the development of area dedicated to this crop, especially in South East Asia, and to some extent in South America and in Africa. In South Asia, where the highest production is recorded in Indonesia, the development of oil palm plantations has often been done at the expense of forests, causing changes in the atmospheric carbon dioxide (CO2) balance due to the land use changes and agricultural management practices. Several studies have emphasized the importance of quantifying the oil palm contribution to the global carbon budget. A Long-term spatial and temporal measurement during its 25-30 years of life-cycle is needed to provide an accurate CO2 balance assessment. One of the advanced methods is to directly measure CO2 fluxes across a relatively large area using a micrometeorological approach based on eddy covariance principles. This method can estimate time series of Net Ecosystem CO2 Exchange (NEE), Gross Primary Production (GPP) and ecosystem respiration (Reco) which are useful to assess carbon balance over an oil palm plantation. For that purpose, a flux tower of 25 m height, fully equipped with micrometeorological instruments, has been installed in 2011 in the center of a 90-ha plot of mature palms planted in Riau Province (Sumatra, Indonesia). The average oil palm canopies height was 18 m with an annual average air temperature of 26°C, 80% air humidity and a 2,500 mm average annual precipitation. The atmospheric conditions, seasonal variations and air pollutants such as haze, heavily influenced the CO2 flux measurement. During this 6 year of study, the mature oil palm agro-system acted as a carbon sink that assimilates CO2 from the atmosphere between 36 to 40 t CO2 ha−1 y−1 as NEE. This result was the balance between emission assimilation of 209 t CO2 ha−1 y−1 (GPP) and release back to the atmosphere of between 138 and 173 t CO2 ha−1 y−1 through respiration (Reco). These variations on the CO2 fluxes were mainly caused by seasonal patterns with a significant contribution of wet and dry days.

Relativistic celestial mechanics at sub-microarcsecond accuracy level

Einstein stated two dictums, so that more experimental facts can replace the previously adopted hypotheses and General Relativity (GR) can evolve to “grand aim” or perfection. In the absence of appropriate experimental facts during pre-CEREPAC (Century-long Experience of Relativity-related Experiments on Physics, Astronomy and Celestial-mechanics) era, Einstein found no “escape” from the consequence of non-Euclidean geometry, while keeping all frames permissible based on contemporary knowledge. Bergmann also stated in 1968 that the “principle of general covariance” has brought about serious complication in GR. During CEREPAC, relativists and mathematical-astronomers invariably identified the appropriate “nature’s preferred-frame,” which was later found essential for operation of conservation laws. Based on CEREPAC, replacing the experimentally unverifiable hypotheses with experimentally proven principles, and improving upon the GR-astronomers model (developed by JPL, USA, as an evolved-version of GR-conventional model) in two successive stages, GR was remodeled to what became evident as Evolved GR (EGR), after it enabled the elimination of all earlier-adopted ad-hoc methods or approaches, and of the problems, paradoxes and anomalies, associated with the applications of GR, during CEREPAC, and after it unraveled the “General-relativistic nature of speed-of-light (c)” which links the variable c r with F r, the local Gravitational Red-Shift Factor (as stated by Einstein between 1911‐1921). As a consequence of the space-age developments in numerical simulation and in the availability of precision observational data, it got proven that nature itself operates the conservation laws of energy, and of linear and angular momentums (both magnitudes and directions), with respect to the appropriate “nature’s preferred frame”; this provided sufficient reason for giving up the “relativity of all frames,” bringing back Euclidean geometry in EGR. Euclidean space in EGR enabled development of a Prototype of future Ephemerides, leading to five orders-of-magnitude improvement in accuracy of computation of precession of celestial orbits, using three independent methods; this methodology of Prototype Ephemeris and “three-methods-match” can also be applied while remaining exclusively within the precincts of GR, by using one alternative mode of running the EGR program for planetary and Lunar orbits, by opting for GRTOPT=Y; this mode utilizes exclusively the GR equations instead of EGR equations; in fact, this mode is the GR-astronomers (modified) model that was really an intermediate stage of evolution (as mentioned above) between the GR-astronomers model and the EGR model. This model incorporates: (1) All good (and, experimentally proven) features from the three generations of GR models (Einstein’s original, Bergmann’s and Misner-Thorne-Wheeler or MTW), and (2) The “Nature-adopted” real orbital model (as proven from comparison of the computed precession values at Micro-arcsecond {μas} level using the “three-methods-match”) for its Methodology for Conservation of Linear and Orbital Angular Momentums, in a polar coordinate system (r, , Φ). This model computes: (1) Precession of celestial orbits at nearly the same accuracy as that done using the EGR model, and (2) About three digit more accurate (than reported by Folkner in 2014, from fitting lunar laser ranging data with an updated lunar gravity field from the GRAIL mission, etc.) orbits of inner planets and the Moon.

Ricci Flow from the Renormalization of Nonlinear Sigma Models in the Framework of Euclidean Algebraic Quantum Field Theory

The perturbative approach to nonlinear Sigma models and the associated renormalization group flow are discussed within the framework of Euclidean algebraic quantum field theory and of the principle of general local covariance. In particular we show in an Euclidean setting how to define Wick ordered powers of the underlying quantum fields and we classify the freedom in such procedure by extending to this setting a recent construction of Khavkine, Melati and Moretti for vector valued free fields. As a by-product of such classification, we prove that, at first order in perturbation theory, the renormalization group flow of the nonlinear Sigma model is the Ricci flow.

Neutrino spin oscillations in external fields in curved spacetime

We study spin oscillations of massive Dirac neutrinos in background matter, electromagnetic and gravitational fields. First, using the Dirac equation for a neutrino interacting with the external fields in curved spacetime, we rederive the quasiclassical equation for the neutrino spin evolution, which was proposed previously basing on principles of the general covariance. Then, we apply this result for the description of neutrino spin oscillations in nonmoving and unpolarized matter under the influence of a constant transverse magnetic field and a gravitational wave. We derive the effective Schr\"odinger equation for neutrino oscillations in these external fields and solve it numerically. Choosing realistic parameters of external fields, we show that the parametric resonance can take place in spin oscillations of low energy neutrinos. Some astrophysical applications are briefly discussed.

Refraction and reflexion according to the principle of general covariance

We show how the principle of general covariance introduced by Souriau in smoothly uniform contexts, can be extended to singular situations, considering the group of diffeomorphisms preserving the singular locus. As a proof of concept, we shall see how we get again, this way, the laws of reflection and refraction in geometric optics, by applying an extended general covariance principle to Riemannian metrics, discontinuous along a hypersurface.