Abstract
We show that the quantum solitons occurring in theories describing a complex scalar field in (1 + 1)-dimensions with a Z(N) symmetry may be identified with sine-Gordon quantum solitons in the phase of this field. Then using both the Euclidean thermal Green function of the two-dimensional free massless scalar field in coordinate space and its dual, we obtain an explicit series expression for the corresponding solitonic correlation function at finite temperature.
Highlights
As remarked in [1], the sine-Gordon (SG) model is certainly one of the best studied of 1 1 -dimensional physics
We show that the quantum solitons occurring in theories describing a complex scalar field in (1 + 1)-dimensions with a Z(N) symmetry may be identified with sine-Gordon quantum solitons in the phase of this field
The interest in this field theoretical model has been enhanced by its connections with the two-dimensional (2D) neutral Coulomb gas (CG) [2] and with the 2D XY-magnetic system [3]
Summary
As remarked in [1], the sine-Gordon (SG) model is certainly one of the best studied of 1 1 -dimensional physics. We may conclude that, in the constant- approximation, the theories given by Equation (1) will present SG solitons in the phase of the complex scalar field. Last but not least, following the above discussion, we may notice that Equation (21) implies that the operator creates eigenstates of the topological charge operator with eigenvalue 2π N (which, not by coincidence, for N 2 , corresponds to the value of the topological charge associated to the classical solitonic excitations presented in Equation (14), namely, π ), proving that the quantum solitons occurring in the theory described by Equation (1) are, SG solitons in the phase of the complex scalar field , i.e. they are phase solitons. We are going to calculate the twopoint correlation function of these quantum soliton excitations at finite temperature
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