Instantons and the spectral function of electrons in the half-filled Landau level
Instantons and the spectral function of electrons in the half-filled Landau level
We calculate the instanton--anti-instanton action ${\mathit{S}}_{\mathit{MM}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}$(\ensuremath{\tau}) in the gauge theory of the half-filled Landau level. It is found that ${\mathit{S}}_{\mathit{MM}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}$(\ensuremath{\tau})=(3-\ensuremath{\eta})[${\mathrm{\ensuremath{\Omega}}}_{0}$(\ensuremath{\eta})\ensuremath{\tau}${]}^{1/(3\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\eta}})}$ for a class of interactions v(q)=${\mathit{V}}_{0}$/${\mathit{q}}^{\mathrm{\ensuremath{\eta}}}$ (0\ensuremath{\le}\ensuremath{\eta}2) between electrons. This means that the instanton--anti-instanton pairs are confining so that a well-defined ``charged'' composite fermion can exist. It is also shown …