% Homework for Physical Mathematics I
% Ewan Stewart
% KAIST
% 2010/10/14

\documentclass[a4paper,12pt]{article}

\usepackage{pm1}

\setcounter{homework}{3}

\begin{document}

\begin{homework}
[Answers should be submitted, as both a tex file and a pdf file, to both me and the teaching assistants. You may use this file as a template.]

\question{MSSM}
The superpotential $W$ of the Minimal Supersymmetric Standard Model is a holomorphic function of $Q$, $u$, $d$, $L$, $e$, $H_u$ and $H_d$ that is invariant under the $\mathrm{U}(1)$ hypercharge symmetry
\begin{equation}
\begin{array}{rcllrcllrcllrcllrcl}
Q & \to & e^{i\theta} Q & ,
& u & \to & e^{-4i\theta} u & ,
& d & \to & e^{2i\theta} d & ,
& L & \to & e^{-3i\theta} L
\\
e & \to & e^{6i\theta} e & ,
& H_u & \to & e^{3i\theta} H_u & ,
& H_d & \to & e^{-3i\theta} H_d
\end{array}
\end{equation}
and the $\Z_2$ $R$-parity symmetry
\begin{equation}
\begin{array}{rcllrcllrcllrcllrcl}
Q & \to & - Q & ,
& u & \to & - u & ,
& d & \to & - d & ,
& L & \to & - L
\\
e & \to & - e & ,
& H_u & \to & H_u & ,
& H_d & \to & H_d
\end{array}
\end{equation}
Expand $W$ in a Taylor series and determine the terms up to cubic order.

\question{sum}
Calculate
\begin{equation}
\sum_{n=0}^\infty x^n
\end{equation}
for $x = 2$.

Use PGF to draw a diagram illustrating your answer.

\end{homework}

\end{document}

