Static knot energy, Hopf charge, and universal growth law

Research output: Contribution to journalArticle

Abstract

We present a family of static knotted soliton energy functionals governing the configuration maps from the Euclidean space R4 n - 1 into the unit sphere S2 n so that the knot charges are naturally represented by the Hopf invariants in the homotopy group π4 n - 1 (S2 n) and the special case n = 1 recovers the classical Faddeev knot energy. We establish the general result that the minimum energy or the knot mass EN of knotted solitons of the Hopf charge N satisfies the universal fractional-exponent growth law EN

Original languageEnglish (US)
Pages (from-to)455-463
Number of pages9
JournalNuclear Physics, Section B
Volume747
Issue number3
DOIs
StatePublished - Jul 24 2006

Fingerprint

solitary waves
Euclidean geometry
functionals
energy
exponents
configurations

Keywords

  • Faddeev knots
  • Hopf fibration
  • Knot energy
  • Skyrme energy
  • Sobolev inequalities
  • Sublinear growth
  • Universality

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Static knot energy, Hopf charge, and universal growth law. / Lin, Fanghua; Yang, Yisong.

In: Nuclear Physics, Section B, Vol. 747, No. 3, 24.07.2006, p. 455-463.

Research output: Contribution to journalArticle

@article{716d7248414f4ced844684c64660ca9e,
title = "Static knot energy, Hopf charge, and universal growth law",
abstract = "We present a family of static knotted soliton energy functionals governing the configuration maps from the Euclidean space R4 n - 1 into the unit sphere S2 n so that the knot charges are naturally represented by the Hopf invariants in the homotopy group π4 n - 1 (S2 n) and the special case n = 1 recovers the classical Faddeev knot energy. We establish the general result that the minimum energy or the knot mass EN of knotted solitons of the Hopf charge N satisfies the universal fractional-exponent growth law EN ∼",
keywords = "Faddeev knots, Hopf fibration, Knot energy, Skyrme energy, Sobolev inequalities, Sublinear growth, Universality",
author = "Fanghua Lin and Yisong Yang",
year = "2006",
month = "7",
day = "24",
doi = "10.1016/j.nuclphysb.2006.05.005",
language = "English (US)",
volume = "747",
pages = "455--463",
journal = "Nuclear Physics B",
issn = "0550-3213",
publisher = "Elsevier",
number = "3",

}

TY - JOUR

T1 - Static knot energy, Hopf charge, and universal growth law

AU - Lin, Fanghua

AU - Yang, Yisong

PY - 2006/7/24

Y1 - 2006/7/24

N2 - We present a family of static knotted soliton energy functionals governing the configuration maps from the Euclidean space R4 n - 1 into the unit sphere S2 n so that the knot charges are naturally represented by the Hopf invariants in the homotopy group π4 n - 1 (S2 n) and the special case n = 1 recovers the classical Faddeev knot energy. We establish the general result that the minimum energy or the knot mass EN of knotted solitons of the Hopf charge N satisfies the universal fractional-exponent growth law EN ∼

AB - We present a family of static knotted soliton energy functionals governing the configuration maps from the Euclidean space R4 n - 1 into the unit sphere S2 n so that the knot charges are naturally represented by the Hopf invariants in the homotopy group π4 n - 1 (S2 n) and the special case n = 1 recovers the classical Faddeev knot energy. We establish the general result that the minimum energy or the knot mass EN of knotted solitons of the Hopf charge N satisfies the universal fractional-exponent growth law EN ∼

KW - Faddeev knots

KW - Hopf fibration

KW - Knot energy

KW - Skyrme energy

KW - Sobolev inequalities

KW - Sublinear growth

KW - Universality

UR - http://www.scopus.com/inward/record.url?scp=33745041692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745041692&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2006.05.005

DO - 10.1016/j.nuclphysb.2006.05.005

M3 - Article

AN - SCOPUS:33745041692

VL - 747

SP - 455

EP - 463

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -