Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAsymptotically Non-Singular Extended Non-Dyonic Solutions of t Hooft-Polyakov Monopole Violates Equations of Motion
311
0
0.0
(
0
)
Authors
K. Rasem Qandalji
Ask ChatGPT about the research
No Arabic abstract
We show that based on the general solution, given by Corrigan, Olive, Fairlie and Nuyts, in the region outside the monopoles core; the equations of motion in the Higgs vacuum (i.e. outside the monopoles core) will not allow asymptotically non-singular extended non-trivial non-Dyonic (including, also, all static) solutions of the t Hooft-Polyakov monopole. In other words, unless the monopoles magnetic charge is shielded (by some mechanism), the Dirac string is inevitable asymptotically, in the region outside the monopoles core, for all non-Dyonic solutions that are admissible by the equations of motion. That we show that the non-dyonic solutions (based on Corrigan et al) will include all admissible static solutions and their gauge transform might be interpreted as that all admissible dyonic solutions (based on Corrigan et al) are composite solutions.
rate research
Read More
Lorentz invariance is broken for the non-Abelian monopoles. Here we will consider the case of t Hooft-Polyakov monopole and show that the Lorentz invariance of its field will be restored using Dirac quantization.
At classical level, dynamical derivation of the properties and conservation laws for topologically non-trivial systems from Noether theorem versus the derivation of the systems properties on topological grounds are considered as distinct. We do celebrate any agreements in results derived from these two distinct approaches: i.e. the dynamical versus the topological approach. Here we consider the Corrigan-Olive-Fairlie-Nuyts solution based on which we study the stability of the t Hooft- Polyakov outer field, known as its Higgs vacuum, and derive its stability, dynamically, from the equations of motion rather than from the familiar topological approach. Then we use our derived result of the preservation of the Higgs vacuum asymptotically to derive the stability of the t Hooft-Polyakov monopole, even if inner core is perturbed, where we base that on observing that the magnetic charge must be conserved if the Higgs vacuum is preserved asymptotically. We also, alternatively, note stability of t Hooft-Polyakov monopole and the conservation of its magnetic charge by again using the result of the Higgs vacuum asymptotic preservation to use Eq.(5) to show that no non-Abelian radiation allowed out of the core as long as the Higgs vacuum is preserved and restored, by the equations of motion, if perturbed. We start by deriving the asymptotic equations of motion that are valid for the monopoles field outside its core; next we derive certain constraints from the asymptotic equations of motion of the Corrigan-Olive-Fairlie-Nuyts solution to the t Hooft-Polyakov monopole using the Lagrangian formalism of singular theories, in particular that of Gitman and Tyutin. The derived constraints will show clearly the stability of the monopoles Higgs vacuum its restoration by the equations of motion of the Higgs vacuum, if disturbed.
The dependence of the energies of axially symmetric monopoles of magnetic charges 2 and 3, on the Higgs self-interaction coupling constant, is studied numerically. Comparing the energy per unit topological charge of the charge-2 monopole with the energy of the spherically symmetric charge-1 monopole, we confirm that there is only a repulsive phase in the interaction energy between like monopoles
We prove, by a shooting method, the existence of infinitely many solutions of the form $psi(x^0,x) = e^{-iOmega x^0}chi(x)$ of the nonlinear Dirac equation {equation*} iunderset{mu=0}{overset{3}{sum}} gamma^mu partial_mu psi- mpsi - F(bar{psi}psi)psi = 0 {equation*} where $Omega>m>0,$ $chi$ is compactly supported and [F(x) = {{array}{ll} p|x|^{p-1} & text{if} |x|>0 0 & text{if} x=0 {array}.] with $pin(0,1),$ under some restrictions on the parameters $p$ and $Omega.$ We study also the behavior of the solutions as $p$ tends to zero to establish the link between these equations and the M.I.T. bag model ones.
We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello it is proved that the profile of the solutions differs from global solutions of a Liouville type equation only by a uniformly bounded term. The present paper improves their result and establishes an expansion of the solutions near the blowup points with a sharp error estimate.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
