### Abstract

The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S^{1}, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range ω ∈ [-1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.

Original language | English |
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Pages (from-to) | 740-754 |

Number of pages | 15 |

Journal | Physics of Atomic Nuclei |

Volume | 74 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1 May 2011 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics

### Cite this

**Q kink of the nonlinear O(3) σ model involving an explicitly broken symmetry.** / Loginov, Yu.

Research output: Contribution to journal › Article

*Physics of Atomic Nuclei*, vol. 74, no. 5, pp. 740-754. https://doi.org/10.1134/S1063778811040107

}

TY - JOUR

T1 - Q kink of the nonlinear O(3) σ model involving an explicitly broken symmetry

AU - Loginov, Yu

PY - 2011/5/1

Y1 - 2011/5/1

N2 - The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S1, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range ω ∈ [-1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.

AB - The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S1, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range ω ∈ [-1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.

UR - http://www.scopus.com/inward/record.url?scp=79957659284&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957659284&partnerID=8YFLogxK

U2 - 10.1134/S1063778811040107

DO - 10.1134/S1063778811040107

M3 - Article

AN - SCOPUS:79957659284

VL - 74

SP - 740

EP - 754

JO - Physics of Atomic Nuclei

JF - Physics of Atomic Nuclei

SN - 1063-7788

IS - 5

ER -