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104 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
105 %%%%%%%%%%%%%%%%%%%%%%% document %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
106 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
113 \includegraphics[scale=1.01,clip]{./hintergrund}
119 % \hfill \includegraphics[width=.1\textwidth]{../../figures/oeaw_logo}
121 \includegraphics[width=.2\textwidth]{./fwf-logo}
128 \fcolorbox{white}{white}
130 \begin{minipage}[b]{400mm}
134 \textcolor{cyan}{\bf Condensation in two flavor scalar electrodynamics with non-degenerate quark masses}}\\[7mm]
135 \Large{\bf{Alexander Schmidt} \sf{, Philippe de Forcrand, Christof Gattringer} \\ \sf{\large University of Graz}}\\\vspace{-1cm}
145 %%%%%%%%%%%%%%%%%%%%%%% 2 columns %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
148 %%%%%%%%%%%%%%%%%%%%%%%%%% Chapter %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
149 % \fcolorbox{black}{kfug-yellow}
151 % \begin{minipage}[b]{350mm}
154 % \large \centering{\textcolor{black}{\LARGE\sf \bf{U(1) Lattice Gauge-Higgs Model}}}
160 \large \centering{\textcolor{cyan}{\LARGE\sf Action}}
164 \begin{minipage}[b]{350mm}
166 The {\bf continuum action} of scalar electrodynamics is given by
168 S = \int{d^4x} \left(\frac{1}{4} |F_{\mu \nu}|^2 + |(\partial_\mu + ieA_\mu)\phi|^2 + m^2(\phi^* \phi) + \lambda(\phi^* \phi)^2\right) \quad ,
170 where $e$ is the gauge coupling, $m$ the mass of the complex scalar $\phi$ and $\lambda$ the Higgs coupling constant.
174 In the conventional notation the {\bf lattice action} is given by (the lattice constant is set to $a=1$)
176 S &=& S_G[U] + S_H[U,\phi] \label{latac} \\ \nonumber \\
177 S_G &=& -\beta \sum_{x,\nu < \rho} \Re{\left(U_{\nu\rho}(x)\right)}, \quad \beta=\frac{1}{2e^2} \nonumber \\ \nonumber \\
178 S_H &=& \sum_x \left[- \frac{1}{2} \sum_{\mu=1}^4 \left( \phi(x)^* U_\mu(x) \phi(x+\hat{\mu}) + \phi(x)^* U_\mu(x-\hat{\mu})^*\phi(x-\hat{\mu})\right) \right . \nonumber \\
179 && \quad\quad\;\, + \left . \kappa \phi(x)^*\phi(x) + \lambda\left(\phi(x)^*\phi(x)\right)^2 \right], \quad \kappa = \frac{m^2+8}{2} \nonumber \quad . \nonumber
182 % \begin{wrapfigure}{r}{0.5\textwidth}
184 % \includegraphics[width=0.49\columnwidth]{sine}
186 % \caption{This is the sine function.}\label{fig1}
193 %%%%%%%%%%%%%%%%%%%%%%%%%% Acknowledgments %%%%%%%%%%%%%%%%%%%%%%%%%%%%
197 \large \centering{\textcolor{cyan}{\Large\sf Acknowledgments}}
201 \begin{minipage}[b]{350mm}
202 This work was supported by the Austrian Science Fund, FWF, through the Doctoral
203 Program on {\it Hadrons in Vacuum, Nuclei, and Stars} (FWF DK W1203-N16).
206 %%%%%%%%%%%%%%%%%%%%%%%%%% References %%%%%%%%%%%%%%%%%%%%%%%%%%%%
210 \large \centering{\textcolor{cyan}{\Large\sf References}}
214 \begin{minipage}[b]{350mm}
220 % \bibliographystyle{h-physrev}
221 % \bibliography{lgt.bib}
224 \end{multicols}\vspace{-24pt}