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Register a new userInteraction Energy of `t Hooft-Polyakov Monopoles
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Authors
B. Kleihaus NUIn Maynooth
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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
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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.
We study monopoles and corresponding t Hooft tensor in a generic gauge theory. This issue is relevant to the understanding of color confinement.
We study monopoles and corresponding t Hooft tensor in QCD with a generic compact gauge group. This issue is relevant to the understanding of color confinement in terms of dual symmetry.
We consider pure Yang Mills theory on the four torus. A set of non-Abelian transition functions is presented which encompass all instanton sectors. It is argued that these transition functions are a convenient starting point for gauge fixing. In particular, we give an extended Abelian projection with respect to the Polyakov loop, where $A_0$ is independent of time and in the Cartan subalgebra. In the non-perturbative sectors such gauge fixings are necessarily singular. These singularities can be restricted to Dirac strings joining monopole and anti-monopole like ``defects.
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