Quantum-statistical mechanics of extended objects. I. Kinks in the one-dimensional sine-Gordon system

Making use of thermal-Green's-function technique, we study the quantum-statistical mechanics of a sine-Gordon system in 1 + 1 dimensions. In the weak-coupling limit, the temperature dependences of the soliton energy, $E_s$, the soliton inertial mass, and the soliton density are determined. At high temperatures ($T>m$, where $m$ is the mass of the fundamental field), $E_s$ decreases monotonically as the temperature increases, and $E_s$ jumps to zero around $T=T_{\mathrm{cr}}$ ($\equiv e^{-1\mathrm{}}{E_s}^0$), where ${E_s}^0$ is the soliton energy at $T=0\mathrm{}$ K. The soliton density agrees with the classical statistical-mechanics results for $T_{\mathrm{cr}}>T\gg m$, if $E_s$ in the classical theory is replaced by the temperature-dependent one of the present theory.