Searcharxiv⌕ Search

arXiv subjects

George Savvidy

Publications and source records attributed to George Savvidy.

At least 19 recordsLinked to original sources
arXiv2026

Absorption of Gravitons and Photon Luminosities of Interstellar/Intergalactic Hydrogen Atoms

We compute the emission and absorption rates of gravitons by hydrogen atoms. The absorption rate of gravitons is proportional to the number of hydrogen atoms and to the graviton luminosity. The number of hydrogen atoms in interstellar/intergalactic media can be large while the graviton luminosity of Sun, or a typical star, is in the eV to keV range that well overlaps with the resonance frequencies of the hydrogen atoms. Currently, the observational knowledge of the graviton luminosity in different regions of the Universe is limited, and here we will consider its value as unknown quantity that should be determined by independent astrophysical observations. We suggest measuring the ratio of the photon luminosities from interstellar/intergalactic hydrogen atoms that can provide information concerning the luminosity of gravitons in different regions of space. This ratio maximally exposes the fundamental physical nature of photons and gravitons - their helicity, which is one for the photons and two for the gravitons. The ratio is sensitive to any sources of gravitational radiation and provide a possible method for measuring their radiation intensities.

hep-ph↗
arXiv2026

QCD Effective Lagrangian and Condensation of Chromomagnetic Flux Tubes

We compute the effective action for covariantly constant gauge fields that are solutions of the sourceless Yang-Mills equation and have the form of magnetic flux tubes. They represent a superposition of infinite many alternating monopole/ani-monopole pairs situated at infinity, with each pair having a structure similar to the Nielsen-Olesen magnetic flux tube. The chromomagnetic flux tubes condensation is stable and indicates that the Yang-Mills vacuum state is highly degenerate.

hep-th↗
arXiv2025

Schwinger's non-commutative coordinates and duality between helicity and Dirac quantisation conditions

The helicity operator of massless particles has only two polarisations like it takes place for photons and gravitons. For them not all of the 2s+1 spin magnetic quantum states exist, with two exceptions, and the spin operator ceases to be defined properly and consistently. The problem was solved by Schwinger, who introduced non-commutative space coordinates that completely eliminate the spin operator and ensure that only helicity operator appears explicitly. We further investigate the violation of the associativity relation of the momentum translation operator that emerges due to the failure of the corresponding Jacobi identity. The associativity relation is broken by a phase factor which satisfies a 3-cocycle relation. The associativity is restored when a 3-cocycle is an integer number, and leads to the quantisation of massless particle's helicity. We discuss the correspondence (duality) between the helicity and the Dirac quantisation conditions. The relation for the minimal space cell volume, similar to the minimal phase-space cell of Heisenberg is suggested.

hep-th↗
arXiv2025

Landscape of QCD Vacuum

We found new solutions of the sourceless Yang-Mills equation describing the superposition of chromomagnetic vortices of oppositely oriented magnetic fluxes. These gauge field configurations have constant energy densities and are separated by potential barriers forming a complicated landscape. It is suggested that the solutions describe the condensate of chromomagnetic vortices and represent a dual analog of the Cooper pairs condensate in a superconductor. In the presence of an Abelian field and in a particular limit the solutions reduce to the flat connections of zero energy density and are forming a complicated potential landscape of the QCD vacuum. A possible tunnelling transition between these superfluxon flat configurations and the flat configurations with non-vanishing Chern-Pontryagin index will wash out the CP violating $θ$ angle to zero, dynamically restoring CP symmetry.

hep-th↗
arXiv2024

Condensation of Magnetic Fluxes and Landscape of QCD Vacuum

I discuss new non-perturbative solutions of the sourceless Yang-Mills equation representing the superposition of oppositely oriented chromomagnetic flux tubes (vortices) similar in their form to a lattice of superposed Abrikosov-Nielsen-Olesen chromomagnetic vortices. These solutions represent highly degenerate classical vacua of the Yang Mills theory that are separated by potential barriers and are forming a complicated potential landscape of the QCD vacuum. It is suggested that the solutions describe a lattice of dense chromomagnetic vortices representing a dual analog of the Cooper pairs condensate in a superconductor.

hep-th↗
arXiv2024

Lars Brink Colleague, Friend and Collaborator

The Landau-Nordita conference that was held in Moscow in 1981 was the first place where I met Lars. This "marvellous meeting", as Lars quoted in one of his reminiscence article, was organised by Alan Luther. It was an event that generated a long-lasting friendship of scientists from East and West, provided a background for the future collaborations and, in particular, my own collaboration with Lars on a supersymmetric high-spin extension of the Poincaré group.

hep-th↗
arXiv2024

Caustics in Self-gravitating N-body systems and Cosmological Large Scale Structures

In this paper we demonstrate the generation of gravitational caustics that appear due to the geodesic focusing in a self-gravitating N-body system. The gravitational caustics are space regions where the density of particles is higher than the average density in the surrounding space. It is suggested that the intrinsic mechanism of caustics generation is responsible for the formation of the cosmological Large Scale Structure that consists of matter concentrations in the form of galaxies, galactic clusters, filaments, and vast regions devoid of galaxies. In our approach the dynamics of a self-gravitating N-body system is formulated in terms of a geodesic flow on a curved Riemannian manifold of dimension 3N equipped by the Maupertuis's metric. We investigate the sign of the sectional curvatures that defines the stability of geodesic trajectories in different parts of the phase space. The regions of negative sectional curvatures are responsible for the exponential instability of geodesic trajectories, deterministic chaos and relaxation phenomena of globular clusters and galaxies, while the regions of positive sectional curvatures are responsible for the gravitational geodesic focusing and generation of caustics. By solving the Jacobi and the Raychaudhuri equations we estimated the characteristic time scale of generation of gravitational caustics, calculated the density contrast on the caustics and compared it with the density contrasts generated by the Jeans-Bonnor-Lifshitz-Khalatnikov gravitational instability and that of the spherical top-hat model of Gunn and Gott.

hep-th↗
arXiv2024

How Large is the Space of Covariantly Constant Gauge Fields

The covariantly constant gauge fields are solutions of the sourceless Yang-Mills equation and represent the classical vacuum fields. We found that the moduli space of covariantly constant gauge fields is much larger than the space of constant chromomagnetic fields. A wider class of covariantly constant gauge field solutions representing non-perturbative magnetic flux sheets of finite thickness is obtained through the nontrivial space-time dependence of a unit colour vector. In some sense these solutions are similar to the Nielsen-Olesen magnetic flux tubes, but instead they have geometry of magnetic flux sheets and are supported without presence of any Higgs field. The infinitesimally thin magnetic sheet solutions can be associated with the singular surfaces considered by 't Hooft. The nonlocal operators that are supported on a two-dimensional surface rather than a one-dimensional curve were considered in literature. These surface operators are analogous to Wilson W(C) and 't Hooft line operators M(C) except that they are supported on a two-dimensional surface rather than a one-dimensional curve. The class of non-perturbative solutions representing a nonvanishing chromomagnetic field that fills out the whole 3D-space is obtained as well. This new class of covariantly constant gauge field solutions is constructed by using the general properties of the Cho Ansatz. We define the topological currents and the corresponding charges and demonstrate that the new solutions have a zero monopole charge density. Instead, the solutions have a nonzero Hopf invariant, which is the magnetic helicity of the Faraday force lines.

hep-th↗
arXiv2023

Stability of Yang Mills Vacuum State

We examine the phenomena of the chromomagnetic gluon condensation in the Yang-Mills theory and the problem of stability of the chromomagnetic vacuum fields. The apparent instability of the chromomagnetic vacuum fields is a result of quadratic approximation. The stability is restored when the nonlinear interaction of negative/unstable modes is taken into account in the case of chromomagnetic vacuum fields and the interaction of the zero modes in the case of (anti)self-dual covariantly-constant vacuum fields. All these vacuum fields are stable and indicate that the Yang-Mills vacuum is highly degenerate quantum state.

hep-th↗
arXiv2023

Yang-Mills Effective Lagrangian. Contribution of Leutwyler Zero Mode Chromons

Recently we calculated the contribution of Leutwyler zero mode chromons to the Yang-Mills effective Lagrangian by integrating over collective coordinates of the nonlinearly interacting zero modes. Here we analyse the behaviour of the partition function prefactor and the integration measure Jacobian of the zero modes and show that these factors do not contribute to the effective Lagrangian.

hep-th↗
arXiv2022

Gauge Field Theory Vacuum and Cosmological Inflation

The deep interrelation between elementary particle physics and cosmology manifests itself when one considers the contribution of quantum fluctuations of vacuum fields to the dark energy and the effective cosmological constant. The contribution of zero-point energy exceeds by many orders of magnitude the observational cosmological upper bound on the energy density of the universe. Therefore it seems natural to expect that vacuum fluctuations of the fundamental fields would influence the cosmological evolution in any way. Our aim in this review article is to describe a recent investigation of the influence of the Yang-Mills vacuum polarisation and of the chromomagnetic condensation on the evolution of Friedmann cosmology, on inflation and on primordial gravitational waves. We derive the quantum energy-momentum tensor and the corresponding quantum equation of state for gauge field theory using the effective Lagrangian approach. The energy-momentum tensor has a term proportional to the space-time metric and provides a finite non-diverging contribution to the effective cosmological constant. This allows to investigate the influence of the gauge field theory vacuum polarisation on the evolution of Friedmann cosmology, inflation and primordial gravitational waves. The Type I-IV solutions of the Friedmann equations induced by the gauge field theory vacuum polarisation provide an alternative inflationary mechanism and a possibility for late-time acceleration. The Type II solution of the Friedmann equations generates the initial exponential expansion of the universe of finite duration and the Type IV solution demonstrates late-time acceleration. The solutions fulfil the necessary conditions for the amplification of primordial gravitational waves.

hep-th↗
arXiv2022

Maximally Chaotic Dynamical Systems and Fundamental Interactions

We give a general review on the application of Ergodic theory to the investigation of dynamics of the Yang-Mills gauge fields and of the gravitational systems, as well as its application in the Monte Carlo method and fluid dynamics. In ergodic theory the maximally chaotic dynamical systems (MCDS) can be defined as dynamical systems that have nonzero Kolmogorov entropy. The hyperbolic dynamical systems that fulfil the Anosov C-condition belong to the MCDS insofar as they have exponential instability of their phase trajectories and positive Kolmogorov entropy. It follows that the C-condition defines a rich class of MCDS that span over an open set in the space of all dynamical systems. The large class of Anosov-Kolmogorov MCDS is realised on Riemannian manifolds of negative sectional curvatures and on high-dimensional tori. The interest in MCDS is rooted in the attempts to understand the relaxation phenomena, the foundations of the statistical mechanics, the appearance of turbulence in fluid dynamics, the non-linear dynamics of Yang-Mills field and gravitating N-body systems as well as black hole thermodynamics. Our aim is to investigate classical- and quantum-mechanical properties of MCDS and their role in the theory of fundamental interactions.

hep-th↗
arXiv2021

Gauge Field Theory Vacuum and Cosmological Inflation without Scalar Field

We derive the quantum energy-momentum tensor and the corresponding quantum equation of state for gauge field theory using the effective Lagrangian approach. The energy-momentum tensor has a term proportional to the space-time metric and provides a finite non-diverging contribution to the effective cosmological term. This allows to investigate the influence of the gauge field theory vacuum polarisation on the evolution of Friedmann cosmology, inflation and primordial gravitational waves. The Type I-IV solutions of the Friedmann equations induced by the gauge field theory vacuum polarisation provide an alternative inflationary mechanism and a possibility for late-time acceleration. The Type II solution of the Friedmann equations generates the initial exponential expansion of the universe of finite duration and the Type IV solution demonstrates late-time acceleration. The solutions fulfil the necessary conditions for the amplification of primordial gravitational waves.

hep-th↗
arXiv2021

Maximally Chaotic Dynamical System of Infinite Dimensionality

We analyse the infinite-dimensional limit of the maximally chaotic dynamical systems that are defined on N-dimensional tori. These hyperbolic systems found successful application in computer algorithms that generate high-quality pseudorandom numbers for advanced Monte Carlo simulations. The chaotic properties of these systems are increasing with $N$ because the corresponding Kolmogorov-Sinai entropy grows linearly with $N$. We calculated the spectrum and the entropy of the system that appears in the infinite dimensional limit. We demonstrated that the limiting system has exponentially expanding and contracting foliations and therefore belongs to the Anosov maximally chaotic dynamical systems of infinite dimensionality. The liming system defines the hyperbolic evolution of the continuous functions very similar to the evolution of a velocity function describing the hydrodynamic flow of fluids. We compare the chaotic properties of the limiting system with those of the hydrodynamic flow of incompressible ideal fluid on a torus investigated by Arnold. This maximally chaotic system can find application in Monte Carlo method, statistical physics and digital signal processing.

nlin.CD↗
arXiv2021

Gravity with Perimeter Action and Gravitational Singularities

We consider the perturbation of the Schwarzschild solution by the perimeter action. The asymptotic behaviour of the solution at infinity and at the horizon are calculated and analysed in the first approximation. The perturbation is characterised by the ratio of the Plank length to the Schwarzschild radius. It is demonstrated that in the modified theory appear space-time regions of the Schwarzschild radius scale that are unreachable by test particles. These regions are located in the places where standard theory of gravity has singularities.

gr-qc↗
arXiv2020

Topological mass generation in four-dimensional gauge theory

The Lagrangian of non-Abelian tensor gauge fields describes the interaction of the Yang-Mills and massless tensor bosons of increasing helicities. We have found a metric-independent gauge invariant density which is a four-dimensional analog of the Chern-Simons density. The Lagrangian augmented by this Chern-Simons-like invariant describes massive Yang-Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory. We present invariant densities which can provide masses to the high rank tensor bosons.

hep-th↗
arXiv2020

Parton Distribution Functions and Tensor Gluons

We further consider a possibility that inside the proton and, more generally, inside the hadrons, there are additional partons - tensor gluons, which can carry a part of the proton momentum. The tensorgluons have zero electric charge, like gluons, but have a larger spin. Inside the proton a nonzero density of the tensorgluons can be generated by the emission of tensorgluons by gluons. The last mechanism is typical for non-Abelian tensor gauge theories. The process of gluon splitting suggests that part of the proton momentum that was carried by neutral partons is shared between vector and tensor gluons. We derive the regularised evolution equations for the parton distribution functions that take into account these new processes. In particular, this will allow to solve numerically the extended DIGLAP equations and to find out the ratio of densities between gluons and tensorgluons.

hep-ph↗