Strange quark matter and proto-strange stars in a baryon density-dependent quark mass model

The properties of strange quark matter and the structures of (proto-)strange stars are studied within the framework of a baryon density-dependent quark mass model, where a new quark mass scaling and self-consistent thermodynamic treatment are adopted. Our results show that the perturbative interaction has a strong impact on the properties of strange quark matter. It is found that the energy per baryon increases with temperature, while the free energy decreases and eventually becomes negative. At fixed temperatures, the pressure at the minimum free energy per baryon is zero, suggesting that the thermodynamic self-consistency is preserved. Additionally, the sound velocity v in quark matter approaches to the extreme relativistic limit (c=p3) as the density increases. By increasing the strengths of confinement parameter D and perturbation parameter C, the tendency for v to approach the extreme relativistic limit at high density is slightly weakened. For (proto-)strange stars, in contrast to the quark mass scalings adopted in previous publications, the new quark mass scaling can accommodate massive proto-strange stars with their maximum mass surpassing twice the solar mass by considering the isentropic stages along the star evolution line, where the entropy per baryon of the star matter was set to be 0.5 and 1 with the lepton fraction Yl=0.4.

Dirac particle in Aharonov–Bohm–Coulomb field: Path integral treatment

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

On the Relativistic Harmonic Oscillator

In view of interest in relativistic harmonic oscillations in media, through which the speed of light is orders of magnitude smaller than in vacuum, the solution of the equation of motion is analyzed in the extreme- and weak-relativistic limits. Using scaled variables, it is shown rigorously how the equation of motion exhibits the characteristics of a boundary-layer problem in the extreme-relativistic limit: The solution differs from a sharp asymptotic pattern only around the turning points of oscillations over a vanishingly small fraction of the period. The sharp asymptotic pattern of the solution is a saw-tooth composed of linear segments. The velocity profile tends to a periodic step function and the phase-space plot tends to a rectangle. An expansion of the solution in terms of a small parameter that measures the proximity to the limit (v/c) → 1 yields an excellent approximation for the solution throughout the whole period of oscillations. In the weak-relativistic limit the same approach yields an approximation to the solution that is significantly better than in traditional asymptotic expansion procedures.

Neutrino Mixing and Oscillations in Quantum Field Theory: A Comprehensive Introduction

We review some of the main results of the quantum field theoretical approach to neutrino mixing and oscillations. We show that the quantum field theoretical framework, where flavor vacuum is defined, permits giving a precise definition of flavor states as eigenstates of (non-conserved) lepton charges. We obtain the exact oscillation formula, which in the relativistic limit reproduces the Pontecorvo oscillation formula and illustrates some of the contradictions arising in the quantum mechanics approximation. We show that the gauge theory structure underlies the neutrino mixing phenomenon and that there exists entanglement between mixed neutrinos. The flavor vacuum is found to be an entangled generalized coherent state of SU(2). We also discuss flavor energy uncertainty relations, which impose a lower bound on the precision of neutrino energy measurements, and we show that the flavor vacuum inescapably emerges in certain classes of models with dynamical symmetry breaking.

Weak Alfvénic turbulence in relativistic plasmas. Part 1. Dynamical equations and basic dynamics of interacting resonant triads

Alfvén wave collisions are the primary building blocks of the non-relativistic turbulence that permeates the heliosphere and low- to moderate-energy astrophysical systems. However, many astrophysical systems such as gamma-ray bursts, pulsar and magnetar magnetospheres and active galactic nuclei have relativistic flows or energy densities. To better understand these high-energy systems, we derive reduced relativistic magnetohydrodynamics equations and employ them to examine weak Alfvénic turbulence, dominated by three-wave interactions, in reduced relativistic magnetohydrodynamics, including the force-free, infinitely magnetized limit. We compare both numerical and analytical solutions to demonstrate that many of the findings from non-relativistic weak turbulence are retained in relativistic systems. But, an important distinction in the relativistic limit is the inapplicability of a formally incompressible limit, i.e. there exists finite coupling to the compressible fast mode regardless of the strength of the magnetic field. Since fast modes can propagate across field lines, this mechanism provides a route for energy to escape strongly magnetized systems, e.g. magnetar magnetospheres. However, we find that the fast-Alfvén coupling is diminished in the limit of oblique propagation.

Non-relativistic ten-dimensional minimal supergravity

We construct a non-relativistic limit of ten-dimensional $$ \mathcal{N} $$ N = 1 supergravity from the point of view of the symmetries, the action, and the equations of motion. This limit can only be realized in a supersymmetric way provided we impose by hand a set of geometric constraints, invariant under all the symmetries of the non-relativistic theory, that define a so-called ‘self-dual’ Dilatation-invariant String Newton-Cartan geometry. The non-relativistic action exhibits three emerging symmetries: one local scale symmetry and two local conformal supersymmetries. Due to these emerging symmetries the Poisson equation for the Newton potential and two partner fermionic equations do not follow from a variation of the non-relativistic action but, instead, are obtained by a supersymmetry variation of the other equations of motion that do follow from a variation of the non-relativistic action. We shortly discuss the inclusion of the Yang-Mills sector that would lead to a non-relativistic heterotic supergravity action.

A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry

We consider a non-relativistic limit of the bosonic sector of eleven-dimensional supergravity, leading to a theory based on a covariant ‘membrane Newton-Cartan’ (MNC) geometry. The local tangent space is split into three ‘longitudinal’ and eight ‘transverse’ directions, related only by Galilean rather than Lorentzian symmetries. This generalises the ten-dimensional stringy Newton-Cartan (SNC) theory. In order to obtain a finite limit, the field strength of the eleven-dimensional four-form is required to obey a transverse self-duality constraint, ultimately due to the presence of the Chern-Simons term in eleven dimensions. The finite action then gives a set of equations that is invariant under longitudinal and transverse rotations, Galilean boosts and local dilatations. We supplement these equations with an extra Poisson equation, coming from the subleading action. Reduction along a longitudinal direction gives the known SNC theory with the addition of RR gauge fields, while reducing along a transverse direction yields a new non-relativistic theory associated to D2 branes. We further show that the MNC theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.

Minimal spin deflection of Kerr-Newman and supersymmetric black hole

Recent studies have shown that minimal couplings for massive spinning particles, which in the classical limit reproduce the leading PM Kerr black hole dynamics, leads to an eikonal S-matrix exhibiting spin-entanglement suppression. In this paper we trace this phenomenon to the suppression of spin-flipping components in the S-matrix, known to be the hallmark of minimal coupling in the ultra-relativistic limit. We further generalize the consideration to charged and $$ \mathcal{N} $$ N = 4 blackholes, demonstrating that in both cases maximal suppression occurs at the extremal limit.

Impact of partially thermal electrons on the propagation characteristics of extraordinary mode in relativistic regime

On employing linearized Vlasov–Maxwell equations the solution of relativistic electromagnetic extraordinary mode is investigated for the wave propagating perpendicular to a uniform ambient magnetic field (in the presence of arbitrary magnetic field limit i.e., ω > Ω > k.v) in partially degenerate (i.e., for T F ≥ T and T ≠ 0) electron plasma under long wavelength limit (ω ≫ k.v). Due to the inclusion of weak quantum degeneracy the relativistic Fermi–Dirac distribution function is expanded under the relativistic limit ( m 0 2 c 2 2 p 2 < 1 $\frac{{m}_{0}^{2}{c}^{2}}{2{p}^{2}}{< }1$ ) to perform momentum integrations which generate the Polylog functions. The propagation characteristics and shifting of cutoff points of the extraordinary mode are examined in different relativistic density and magnetic field ranges. The novel graphical results of extraordinary mode in relativistic quantum partially degenerate (for μ T = 0 $\frac{\mu }{T}=0$ ), nondegenerate (for μ T ≈ − 1 $\frac{\mu }{T}\approx -1$ ) and fully/completely degenerate (for μ T ≈ $\frac{\mu }{T}\approx $ 1) environments are obtained and the previously reported results are retraced as well.

Gravitational decoupling and superfluid stars

The gravitational decoupling is applied to studying minimal geometric deformed (MGD) compact superfluid stars, in covariant logarithmic scalar gravity on fluid branes. The brane finite tension is shown to provide more realistic values for the asymptotic value of the mass function of MGD superfluid stars, besides constraining the range of the self-interacting scalar field, minimally coupled to gravity. Several other physical features of MGD superfluid stars, regulated by the finite brane tension and a decoupling parameter, are derived and discussed, with important corrections to the general-relativistic limit that corroborate to current observational data.