Thermal bosonisation in the sine-Gordon and massive Thirring models



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Gómez Nicola, Ángel and Steer, D. A. (1999) Thermal bosonisation in the sine-Gordon and massive Thirring models. Nuclear physics B, 508 . pp. 409-499. ISSN 0550-3213

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We study bosonisation in the massive Thirring and sine-Gordon models at finite temperature T and non-zero fermion chemical potential μ. For that purpose we use both canonical operator and path-integral approaches, paying particular attention to the issues of thermal normal ordering and renormalisation. At T > 0 and μ = 0, the massive Thirring model bosonises to the sine Gordon model with the same T =0 identification between coupling constants. We prove that not only the partition functions of the two models coincide, as was recently shown, but also that thermal averages of zero-charge operators can be identified. In particular, analysis of the point split regularised fermion current then leads to the thermal equivalence between sine-Gordon kinks and Thirring fermions. At μ ≠ 0, T > 0 and working in perturbation theory about the massless Thirring model, we show that the bosonised theory is the sine-Gordon model plus an additional topological term which accounts for the existence of net fermion charge excitations (the fermions or the kinks) in the thermal bath. This result generalises one recently obtained for the massless case, and it is the two-dimensional version of the low- energy QCD chiral Lagrangian at finite baryon density.

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© 1999 Elsevier Science B.V.
We thank Peter Landshoff both for useful arguments and for originally drawing our attention in this direction. We are grateful to Tim Evans and Ray Rivers for numerous helpful discussions and to R.E Alvarez-Estrada for useful suggestions. A.G.N. has received support through CICYT, Spain, project AEN97-1693 and through a fellowship of MEC, Spain, and would like to thank the Imperial College Theory Group for their hospitality during the completion of this work. D.A.S. is supported by P.P.A.R.C. of the UK through a research fellowship and is a member of Girton College, Cambridge. This work was supported in part by the E.S.E

Uncontrolled Keywords:2 Dimensions; Finite-temperature; Current-algebra; Wicks theorem
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30639
Deposited On:05 Jun 2015 09:22
Last Modified:10 Dec 2018 15:10

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