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Skyrme Sphalerons of an O (3)‐σ Model and the Calculation of Transition Rates at Finite Temperature
Author(s) -
Zimmerschied F.,
Tchrakian D.H.,
Tchrakian D.H.,
MüllerKirsten H.J.W.
Publication year - 1998
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/(sici)1521-3978(199803)46:2<147::aid-prop147>3.0.co;2-h
Subject(s) - sphaleron , physics , antisymmetric relation , measure (data warehouse) , quantum tunnelling , quartic function , coupling (piping) , mathematical physics , path integral formulation , thermal fluctuations , crossover , quantum mechanics , symmetry breaking , sigma model , quantum , phase transition , nonlinear system , mathematics , mechanical engineering , baryogenesis , database , artificial intelligence , computer science , pure mathematics , engineering
The reduced O (3)‐σ model with an O (3)‐σ→ O (2) symmetry breaking potential is considered with an additional Skyrmionic term, i.e. a totally antisymmetric quartic term in the field derivatives. This Skyrme term does not affect the classical static equations of motion which, however, allow an unstable sphaleron solution. Quantum fluctuations around the static classical solution are considered for the determination of the rate of thermally induced transitions between topologically distinct vacua mediated by the sphaleron. The main technical effect of the Skyrme term is to produce an extra measure factor in one of the flucuation path integrals which is therefore evaluated using a measuremodified Fourier‐Matsubara decomposition (this being one of the few cases permitting this explicit calculation). The resulting transition rate is valid in a temperature region different from that of the original Skyrme‐less model, and the crossover from transitions dominated by thermal fluctuations to those dominated by tunneling at the lower limit of this range depends on the strength of the Skyrme coupling.