Type Lagrangian Research Articles

Manifestly covariant polynomial M5-brane lagrangians

We present polynomial and manifestly covariant M5-brane Lagrangians along with their analyses involving their dynamics, gauge symmetries and their nonlinear self-duality condition. Such Lagrangians can be particularly useful for developments that are otherwise hindered by a non-polynomial structure and singularity of the Lagrangian such as its quantisation. Although on integrating out some of the auxiliary fields these polynomial Lagrangians reduce to the M5-brane Lagrangian given by the Pasti-Sorokin-Tonin (PST) formalism, in the analysis of the polynomial Lagrangians the only remnant of the non-polynomial structure of the PST type Lagrangian appears in the gauge transformation corresponding to an infinitesimal shift of a Stückelberg field. This transformation does not affect the dynamics or the on-shell self-duality condition of the polynomial M5-brane Lagrangians.

Search for Manifestations of Spin–Torsion Coupling

We investigate the axial vector spin–torsion coupling effects in the framework of the Poincaré gauge theory of gravity with the general Yang–Mills type Lagrangian. The dynamical equations for the “electric” and “magnetic” components of the torsion field variable are obtained in the general form and it is shown that the helicity density and the spin density of the electromagnetic field appear as the physical sources. The modified Maxwell’s equations for the electromagnetic field are derived, and the electromagnetic wave propagation under the action of the uniform homogeneous torsion field is considered. We demonstrate the Faraday effect of rotation of the polarization for such a wave and establish the strong bound on the possible cosmic axial torsion field from the astrophysical data.

Reconstruction and stability analysis of some cosmological bouncing solutions in F(ℛ,T) theory

This paper investigates the possibility of reconstruction of the generic function in [Formula: see text] gravitational theory by considering some well-known cosmological bouncing models, namely, exponential evaluation, oscillatory, power law and matter bounce model, where [Formula: see text] and [Formula: see text] are Ricci scalar and trace of energy–momentum tensor, respectively. Due to the complexity of dynamical field equations, we propose some ansatz forms of function [Formula: see text] in perspective models and examine which type of Lagrangian is capable of reproducing bouncing solution via analytical expression. It is seen that for some cases of exponential, oscillatory and matter bounce models, it is possible to get analytical solution while in other cases, it is not possible to achieve exact (general) solutions so only complementary solutions can be discussed. However, for power-law model, all forms of generic function can be reconstructed analytically. Next we analyze the energy conditions and stability of these reconstructed cosmological bouncing models which have analytical forms. It is found that these models are stable for linear forms of Lagrangian only but the reconstructed solutions for power law are unstable for some nonlinear forms of Lagrangian. Further, we determine the observable quantities like spectral index ([Formula: see text]) and tensor-to-scalar ratio ([Formula: see text]) for the simplest reconstructed form of [Formula: see text] function. As a result, we directly confront the reconstructed linear form of Lagrangian in [Formula: see text] model with 2018 Planck observations. Furthermore, we analyze that [Formula: see text] gravity with dark energy epoch is consistent with Sne-Ia+BAO+H(z)+CMB data and show that bounce can unify with dark energy epochs in [Formula: see text] gravity.

Moffat MOdified Gravity (MOG)

Scalar Tensor Vector Gravity (STVG) or MOdified Gravity (MOG) is a metric theory of gravity with dynamical scalar fields and a massive vector field introduced in addition to the metric tensor. In the weak field approximation, MOG modifies the Newtonian acceleration with a Yukawa-like repulsive term due to a Maxwell–Proca type Lagrangian. This associates matter with a fifth force and a modified equation of motion. MOG has been successful in explaining galaxy rotation curves, cosmological observations and all other solar system observations without the need for dark matter. In this article, we discuss the key concepts of MOG theory. Then, we discuss existing observational bounds on MOG weak field parameters. In particular, we will present our original results obtained from the X-COP sample of galaxy clusters.

Infinitesimal Time Reparametrisation and Its Applications

A geometric approach to Sundman infinitesimal time-reparametrisation is given and some of its applications are used to illustrate the general theory. Special emphasis is put on geodesic motions and systems described by mechanical type Lagrangians. The Jacobi metric appears as a particular case of a Sundman transformation.

THE LAWS OF MOTION IN GAUGE THEORIES OF GRAVITY

The general theory of relativity (GR) states that the matter that generates the gravitational field cannot move arbitrarily, it must obey certain equations that follow from the equations of the gravitational field as conditions for their compatibility. In this article we analyze the laws of motion of charged matter in gauge theories of gravitation with higher derivatives of field variables. Object: to consider the laws of motion in gauge theories of gravitation. Task to analyze the laws of motion of charged matter in gauge theories of gravitation with higher derivatives of field variables. Conclusions: it is proved that the equation of an arbitrary gauge field of internal symmetry regardless of the specific type of its Lagrangian can be written both in the form of Einstein's equation and in superpotential form, i.e. as an expression of the total current of gauge charges through the superpotential determined by a specific type of Lagrangian that is, in the form of the Young-Mills equations. So this is a consequence of purely-symmetry theory. Also, a statement is proved in which the constraints on the equations of some fields, which follow from the assumption of the equations of motion for other fields. Research perspectives: nowadays, scientists register gravitational waves and analyze the conditions for their emission, and interest in the problem of motion has been renewed. Note that theories of gravity with higher derivatives of field variables in the Lagrangian of the gravitational field (for example, f(R)-theories) have become very popular in the present. Note that on the basis of the laws of motion of charged matter considered in the article in the gauge theory of gravity, it is possible to successfully further investigate the laws of motion in other theories of gravity, which can be useful in various areas of theoretical and experimental physics.

Cosmology of linear Higgs-sigma models with conformal invariance

We consider general linear Higgs-sigma models as ultra-violet completions of the Higgs inflation. We introduce general higher curvature terms beyond Einstein gravity and recast them into a class of linear Higgs-sigma models in the scalar-dual formulation where conformal symmetry is manifest. Integrating out the sigma field in this class of linear sigma models, we obtain the same Higgs inflation Lagrangian of non-linear sigma model type in the effective theory. We show that the successful inflation for sigma field singles out the sigma-field potential derived from the R2 term and the tracker solution for dark energy at late times can be realized for the Rp+1 term with −1 < p < 0. We also discuss the implications of Higgs-sigma interactions for the inflation and the vacuum stability in the Standard Model.

Phase diagram of interacting pion matter and isospin charge fluctuations

Equation of state and electric (isospin) charge fluctuations are studied for matter composed of interacting pions. The pion matter is described by self interacting scalar fields via a $\phi^4-\phi^6$ type Lagrangian. The mean-field approximation is used, and interaction parameters are fixed by fitting lattice QCD results on the isospin density as a function of the isospin chemical potential at zero temperature. Two scenarios for fixing the model parameters -- with and without the first order phase transition -- are considered, both yielding a satisfactory description of the lattice data. Thermodynamic functions and isospin charge fluctuations are studied and systematically compared for these two scenarios, yielding qualitative differences in the behavior of isospin charge susceptibilities. These differences can be probed by lattice simulations at temperatures $T \lesssim 100$ MeV.

Inflationary cosmology- A new approach using Non-linear electrodynamics

We explore a new kind of NLED field as a source of gravity, which can accelerate the Universe during the inflationary era. We propose a new type of NLED lagrangian which is characterised by two parameters: α (dimensionless parameter) and β (dimensionful parameter). We investigate the classical stability and the causality aspects of this model of inflationary expansion by demanding that the speed of the sound wave and . Corresponding to , we find for α = 0.1(1.0). The equation of state parameter ω = −1/3 requires corresponding to . We find that the Universe is accelerating i.e. (which results in the deceleration parameter q < 0 (i.e. ω > −1/3)), provided . During inflation, the energy density is found to be maximum and is given by . The magnetic field necessary to trigger the inflation is found to be , where is the energy density of the Universe during the inflationary expansion. Our model also predicts the e-fold number that the magnetic field at the end of inflation is about B = 10−10 (10−4) Gauss corresponding to z = 0(1000) and this agrees quite well with the experimental prediction of the e-fold number. With α = 0.3(1.0) and , we find the scalar spectral index n s = 0.9649, consistent with the PLANCK 2018 CMB data. Further, with , we predicts the tensor-to-scalar ratio r = 0.1417(0.1449) and the tensorial spectral index .

△S=1 Weak Transitions in Skyrme model Generalized up to Quartic Terms

&lt;p&gt;We investigate △S=1 weak transition in the light of most general Skyrme type lagrangian containing terms up to quartic terms in field gradients. The additional parameters in the lagrangian are taken from pion-pion scattering data. Our decay amplitudes for anticommutator term in the Skyrme lagrangian shows much improvement over the Skyrme values. S-wave decay amplitudes are also reasonably reproduced in the model.&lt;/p&gt;

Finite element analysis of an arbitrary Lagrangian–Eulerian method for Stokes/parabolic moving interface problem with jump coefficients

In this paper, a type of arbitrary Lagrangian–Eulerian (ALE) finite element method in the monolithic frame is developed for a linearized fluid–structure interaction (FSI) problem — an unsteady Stokes/parabolic interface problem with jump coefficients and moving interface, where, the corresponding mixed finite element approximation in both semi- and fully discrete scheme are developed and analyzed based upon one type of ALE formulation and a novel H1-projection technique associated with a moving interface problem, and the stability and optimal convergence properties in the energy norm are obtained for both discretizations to approximate the solution of a transient Stokes/parabolic interface problem that is equipped with a low regularity. Numerical experiments further validate all theoretical results. The developed analytical approaches and numerical implementations can be similarly extended to a realistic FSI problem in the future.

Thermodynamics for the k-essence emergent Reissner–Nordstrom–de Sitter spacetime

The {\bf k-}essence emergent Reissner-Nordstrom-de Sitter spacetime has exactly mapped on to the Robinson-Trautman (RT) type spacetime with cosmological constant $\L$ for certain configuration of {\bf k-}essence scalar field. Theoretically, we evaluated that the thermodynamical quantities for the RT type emergent black hole is different from the usual one in the presence of kinetic energy of the {\bf k-}essence scalar field i.e., the dark energy density. We restrict ourselves into the fact that the dark energy density (K) is to be unity, then the effective temperature and pressure both are negative for the RT type emergent black hole which implies that the system is thermodynamically unstable when the charge $Q\neq 0$ and the emergent spacetime is only dark energy dominated and it does not radiate when $Q=0$. The thermodynamically unstable situation is physically plausible only when we consider spin degrees of freedom of a system. We have made this analysis in the context of dark energy in an emergent gravity scenario having {\bf k-}essence scalar fields $\phi$ with a Dirac-Born-Infeld type lagrangian. The scalar field also satisfies the emergent equation of motion at $r\rightarrow\infty$.

The Hawking temperature in the context of dark energy for Kerr\u2013Newman and Kerr\u2013Newman\u2013AdS backgrounds

We show that the Hawking temperature is modified in the presence of dark energy in an emergent gravity scenario for Kerr–Newman(KN) and Kerr–Newman–AdS(KNAdS) background metrics. The emergent gravity metric is not conformally equivalent to the gravitational metric. We calculate the Hawking temperatures for these emergent gravity metrics along theta =0. Also we show that the emergent black hole metrics are satisfying Einstein’s equations for large r and theta =0. Our analysis is done in the context of dark energy in an emergent gravity scenario having k-essence scalar fields phi with a Dirac–Born–Infeld type Lagrangian. In KN and KNAdS background, the scalar field phi (r,t)=phi _{1}(r)+phi _{2}(t) satisfies the emergent gravity equations of motion at rrightarrow infty for theta =0.

Exact Solutions in Poincaré Gauge Gravity Theory

In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are naturally identified with the torsion and the curvature on the Riemann–Cartan spacetime. We study the class of quadratic Poincaré gauge gravity models with the most general Yang–Mills type Lagrangian which contains all possible parity-even and parity-odd invariants built from the torsion and the curvature. Exact vacuum solutions of the gravitational field equations are constructed as a certain deformation of de Sitter geometry. They are black holes with nontrivial torsion.

On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories

Recently, it was found that certain 4d mathcal{N}=1 Lagrangians experience supersymmetry enhancement at their IR fixed point, thereby giving a Lagrangian description for a plethora of Argyres-Douglas theories. A generic feature of these Lagrangians is that a number of gauge invariant operators decouple (as free fields) along the RG-flow. These decoupled operators can be naturally taken into account from the beginning itself by introducing additional gauge singlets (sometimes called “flipping fields”) that couple to the decoupled operators via appropriate superpotential terms. It has also been checked that upon dimensionally reducing to 3d, the (A1, A2n−1) type Lagrangians only produce the expected behavior when flipping fields are included in the Lagrangian. In this paper we further investigate the role of flipping fields and find an example where the expected necessity of including the flipping fields in the dimensionally reduced Lagrangians seems to get violated. In the process we find two new dual Lagrangians for the so called 3d T [SU(2)] theory.

Higgs fields induced by Yang–Mills type Lagrangians on gauge-natural prolongations of principal bundles

We address some new issues concerning spontaneous symmetry breaking. We define classical Higgs fields for gauge-natural invariant Yang–Mills type Lagrangian field theories through the requirement of the existence of canonical covariant gauge-natural conserved quantities. As an illustrative example, we consider the ‘gluon Lagrangian’, i.e. a Yang–Mills Lagrangian on the [Formula: see text]-order gauge-natural bundle of [Formula: see text]-principal connections, and canonically define a ‘gluon’ classical Higgs field through the split reductive structure induced by the kernel of the associated gauge-natural Jacobi morphism.

Singularities in particle-like description of FRW cosmology

In this paper, we apply the method of reducing the dynamics of FRW cosmological models with a barotropic form of the equation of state to the dynamical system of the Newtonian type to detect the finite scale factor singularities and the finite-time singularities. In this approach all information concerning the dynamics of the system is contained in a diagram of the potential function V(a) of the scale factor. Singularities of the finite scale factor make themselves manifest by poles of the potential function. In our approach the different types of singularities are represented by critical exponents in the power-law approximation of the potential. The classification can be given in terms of these exponents. We have found that the pole singularity can mimic an inflation epoch. We demonstrate that the cosmological singularities can be investigated in terms of the critical exponents of the potential function of the cosmological dynamical systems. We assume that the general form of the model contains matter and some kind of dark energy which is parameterised by the potential. We distinguish singularities (by an ansatz involving the Lagrangian) of the pole type with the inflation and demonstrate that such a singularity can appear in the past.

A first-order approach to conformal gravity

We investigate whether a spontaneously-broken gauge theory of the group may be a viable alternative to general relativity. The basic ingredients of the theory are an gauge field and a Higgs field W in the adjoint representation of the group with the Higgs field producing the symmetry breaking . The action for gravity is polynomial in and the field equations are first-order in derivatives of these fields. The new symmetry in the gravitational sector is interpreted in terms of an emergent local scale symmetry and the existence of ‘conformalized’ general relativity and fourth-order Weyl conformal gravity as limits of the theory is demonstrated. Maximally symmetric spacetime solutions to the full theory are found and stability of the theory around these solutions is investigated; it is shown that regions of the theory’s parameter space describe perturbations identical to that of general relativity coupled to a massive scalar field and a massless one-form field. The coupling of gravity to matter is considered and it is shown that Lagrangians for all fields are naturally gauge-invariant, polynomial in fields and yield first-order field equations; no auxiliary fields are introduced. Familiar Yang–Mills and Klein–Gordon type Lagrangians are recovered on-shell in the general-relativistic limit of the theory. In this formalism, the general-relativistic limit coincides with a spontaneous breaking of scale invariance and it is shown that this generates mass terms for Higgs and spinor fields.

Statistical Contact Model for Confined Molecules

A theory that describes in a realistic form a system of atoms under the effects of temperature and confinement is presented. The theory departs from a Lagrangian of the Zwanzig type and contains the main ingredients for describing a system of atoms immersed in a heat bath that is also formed by atoms. The equations of motion are derived according to Lagrangian mechanics. The application of statistical mechanics to describe the bulk effects greatly reduces the complexity of the equations. The resultant equations of motion are of the Langevin type with the viscosity and the temperature of the heat reservoir able to influence the trajectories of the particles. The pressure effects are introduced mechanically by using a container with an atomic structure immersed in the heat bath. The relevant variables that determine the equation of state are included in the formulation. The theory is illustrated by the derivation of the equation of state for a system with 76 atoms confined inside of a 180-atom fullerene-like cage that is immersed in fluid forming the heat bath at a temperature of 350 K and with the friction coefficient of 3.0 \( \mathrm{{ps}}^{-1}\). The atoms are of the type believed to form the cores of the Uranus and Neptune planets. The dynamic and the static pressures of the confined system are varied in the 3–5 KBar and 2–30 MBar ranges, respectively. The formulation can be equally used to analyze chemical reactions under specific conditions of pressure and temperature, determine the structure of clusters with their corresponding equation of state, the conditions for hydrogen storage, etc. The theory is consistent with the principles of thermodynamics and it is intrinsically ergodic, of general use, and the first of this kind.

Special modes in a two-sector economy model with an integral utility function

In this work, we study a two-sector economic model with the Cobb–Douglas production function on an infinite planning horizon where the utility function is a functional of an integral form and a Lagrangian of a logarithmic type. A one-dimensional equation is obtained that depends only on the coefficients of elasticity and amortization, and determines the possible special modes. The special modes are described in analytical form.