My additions were these 2 lines:

\usepackage[textmath,displaymath,footnotes,sections,floats]{preview}
\PreviewMacro*[?[{@{[]}}{}]{\pcase}

where \PreviewMacro* tell preview how to deal your \pcase macro.  I
think the result is what you have expected, therefore I'm closing this
report.

Best, Arash