}d\tau \int d{\bf x}%
G\left( \tau ,{\bf x}\right) e^{i\left( p_{4}\tau -{\bf px}\right) } 
\eqnum{2.16}$$

can be expressed in terms of the orthonormalized harmonic oscillator wave functions $\varphi _{n}\left( \xi \right) $ as [@Efrain]

$$\begin{aligned}
G\left( p_{4},{\bf p}\right) &=&\int\limits_{0}^{\infty }d\rho
\int\limits_{-\infty }^{\infty }dx_{2}\sqrt{\overline{b}}\exp -\left(
ip_{2}x_{2}\right) \exp -\left( ip_{4}+\mu -\frac{\overline{b}}{2m}\right)
\rho  \nonumber \\
&&\sum\limits_{n=0}^{\infty }\varphi _{n}\left( \xi \right) \varphi
_{n}\left( \xi ^{\prime }\right) t^{n}  \eqnum{2.17}\end{aligned}$$

where $t=\exp \frac{\overline{b}}{m}\rho $, $\xi =\frac{p_{1}}{\sqrt{%
\overline{b}}}+\frac{x_{2}\sqrt{\overline{b}}}{2}$, $\xi ^{\prime }=\frac{%
p_{1}}{\sqrt{\overline{b}}}-\frac{x_{2}\sqrt{\overline{b}}}{2}$ and $%
p_{4}=(2n+1)\pi /\beta $ are the discrete frequencies $(n=0,1,2,...)$ corresponding to fermion fields.

Linear Response in the Infinite Strip
=====================================

Effective Theory at $\mu \neq 0$ and $T\neq 0$
----------------------------------------------

In ref.[@8] the effective current-current interaction of the MCS model was calculated to determine the independent components of the magnetic interaction at finite temperature in a sample without boundaries, i.e., in the free space. These authors concluded that the pure Meissner effect observed at zero temperature is certainly compromised by the appearance of a long-range mode at $T\neq 0$. Our main goal in the present paper is to investigate the magnetic response of the charged anyon fluid at finite temperature for a sample that confines the fluid within some specific boundaries. As we prove henceforth, 