### Abstract

We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.

Original language | English (US) |
---|---|

Pages (from-to) | 338-353 |

Number of pages | 16 |

Journal | Nuclear Physics, Section B |

Volume | 901 |

DOIs | |

State | Published - Dec 1 2015 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*901*, 338-353. https://doi.org/10.1016/j.nuclphysb.2015.10.017

**Towards a quantum theory of solitons.** / Dvali, Gia; Gomez, Cesar; Gruending, Lukas; Rug, Tehseen.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 901, pp. 338-353. https://doi.org/10.1016/j.nuclphysb.2015.10.017

}

TY - JOUR

T1 - Towards a quantum theory of solitons

AU - Dvali, Gia

AU - Gomez, Cesar

AU - Gruending, Lukas

AU - Rug, Tehseen

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.

AB - We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.

UR - http://www.scopus.com/inward/record.url?scp=84946593770&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946593770&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2015.10.017

DO - 10.1016/j.nuclphysb.2015.10.017

M3 - Article

AN - SCOPUS:84946593770

VL - 901

SP - 338

EP - 353

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -