DOI: 10.1051/jp1:1992121
J. Phys. I France 2 (1992) 23-29

Zero modes and commensurate-incommensurate transitions

C. Mantea¹, A. Corciovei², A. Stepanescu³ and A. Masoero<sup>1

1</sup>  Research Institute for Electrical Engineering (ICPE), Bucharest, Bd. T. Vladimirescu, 45-47, Romania
²  Department of Fundamental Physics, Institute for Physics and Nuclear Engineering, Mägurele, Bucharest, MG-6, Romania
³  Dipartamento di Fisica and I.N.F.M.-C.I.S.M., Politecnico di Torino, C. so Duca degli Abruzzi 24, 10129 Torino, Italy

(Received 22 April 1991, revised 19 August 1991, accepted 23 September 1991)

Abstract
There are two different results concerning the functional relationship between the chemical potential of the 1D massive Thirring model and the misfit parameter of the 1D quantum sine-Gordon model which have been reported [4-7]. In order to investigate this problem, the Jordan boson representation of fermion field operators is used to obtain the bosonized expression of the 1D massive Thirring model. The equivalence of this model with the 1D quantum sine-Gordon model is proved, all zero-mode contributions taken into account. The problem of controversial results previously reported is solved. Thereafter, by means of Bethe-Ansatz method, a new expression for the critical curve of the commensurate-incommensurate transition in the two-dimensional sine-Gordon model is found.

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