[XeTeX] Problem with greek characters in math

[gmoutsin at physics.auth.gr]

I should say in advance that i have almost no experience with Tex. So my problem
is the following.

When i compile this:

\documentclass{article}
\begin{document}
abcdef (line 1) \newline
αβγδεζ (line 2) \newline
$ \alpha \beta \gamma \delta \epsilon \zeta$ (line 3)
\end{document}

logically i get the first and the third line correct but not the second (the
second has the same greek letters as in the math mode).


However when i use:

\documentclass{article}
\usepackage{fontspec}
\usepackage{xunicode}
\usepackage{xltxtra}
\setromanfont{FreeSerif}
\setsansfont{FreeSans}
\setmonofont{FreeMono}
\setmainfont{DejaVuSans}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{latexsym}
\begin{document}
abcdef (line 1) \newline
αβγδεζ (line 2) \newline
$ \alpha \beta \gamma \delta \epsilon \zeta$ (line 3)
\end{document}

I get correctly the first two lines but nothing in the math mode.

i'm totally confused with this and any help is more than welcome.