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Existence of Julia-Zee dyon and 't Hooft-Polyakov monopole with new field strength tensor

Lei Cao, Yilu Xu

Abstract

In this paper, we use a modified Abelian field strength tensor in Georgi-Glashow model and obtain a new Julia-Zee dyon equations which degenerated into the 't Hooft-Polyakov monopole equations when the profile function J=0. Combining a three-step iterative shooting argument and a fixed-point theorem approach, we establish the existence of the static solution of the Julia-Zee dyon equations and discuss its qualitative properties. In addition, we show that the total magnetic charge is a constant related to the gauge coupling constant and the total electric charge depend continuously on the profile functions.

Existence of Julia-Zee dyon and 't Hooft-Polyakov monopole with new field strength tensor

Abstract

In this paper, we use a modified Abelian field strength tensor in Georgi-Glashow model and obtain a new Julia-Zee dyon equations which degenerated into the 't Hooft-Polyakov monopole equations when the profile function J=0. Combining a three-step iterative shooting argument and a fixed-point theorem approach, we establish the existence of the static solution of the Julia-Zee dyon equations and discuss its qualitative properties. In addition, we show that the total magnetic charge is a constant related to the gauge coupling constant and the total electric charge depend continuously on the profile functions.
Paper Structure (7 sections, 5 theorems, 117 equations)

This paper contains 7 sections, 5 theorems, 117 equations.

Table of Contents

  1. Introduction
  2. Julia--Zee dyon and 't Hooft--Polyakov monopole
  3. Proof of existence result
  4. The equation governing the $F$--component
  5. The equation governing the $h$--component
  6. The equation governing the $J$--component
  7. Proof of solution to the full equations

Key Result

Theorem 2.1

For any $\lambda>0$ and $0\leq C<1$, the non--Abelian gauge field equations 2.1g--2.1i have a finite--energy static solution $(\mathbf{A_{\mu}},\phi)$ defined by 2.1d--2.1f so that the obtained solution configuration functions of the radially symmetric Julia-Zee dyon equations 2.2--2.4 have the foll and a magnetic charge $q_m=1/2g$.

Theorems & Definitions (8)

  • Theorem 2.1
  • Theorem 2.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof