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Prog. Theor. Phys. Vol. 83 No. 1 (1990) pp. 118-133

Sphalerons of O(3) Nonlinear Sigma Model on a Circle

Koichi Funakubo, Shoichiro Otsuki^* and Fumihiko Toyoda^**

Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo 188
^*Department of Physics, Kyushu University 33, Fukuoka 812
^**Department of Liberal Arts, Kinki University in Kyushu, Iizuka 820

(Received September 11, 1989)

Abstract:

A series of saddle point solutions of O(3) nonlinear sigma model with symmetry breaking term in 1+1 dimensions are obtained by imposing boundary condition either periodic or partially antiperiodic (O(3) sphalerons on a circle). Under the periodic boundary condition, classical features of the O(3) sphalerons are similar to scalar sphalerons of φ⁴ model on a circle by Manton and Samols. Under the partially antiperiodic boundary condition, the lowest of the O(3) sphalerons coincides in the limit of infinite spatial domain with the O(3) sphaleron by Mottola and Wipf. In particular, zero and negative modes of them are examined in detail. An estimate of transition rate over the lowest O(3) sphaleron at finite temperature is made, and some remarks on simulating the transition on a lattice are given. A correspondence between these O(3) sphalerons on a circle and a series of (possible) classical solutions of SU(2) gauge-Higgs model, to which the electroweak sphaleron S and new sphaleron S^* belong, is discussed.

URL : http://ptp.ipap.jp/link?PTP/83/118/
DOI : 10.1143/PTP.83.118

[ Full Text PDF : FREE ACCESS (796K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 84 No. 6 (1990) pp. 1196-1211 :

   Sphaleron Transition of Reduced O(3) Nonlinear Sigma Model

   Koichi Funakubo, Shoichiro Otsuki and Fumihiko Toyoda

2. Progress of Theoretical Physics Vol. 88 No. 3 (1992) pp. 571-584 :

   Fluctuating Fields at a Sphaleron and a Generalized Levinson Theorem

   Tomoya Akiba, Jousuke Kuroiwa and Jun-ichi Kakizaki

3. Progress of Theoretical Physics Vol. 96 No. 3 (1996) pp. 475-519 :

   CP Violation and Baryogenesis at the Electroweak Phase Transition

   Koichi Funakubo

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