Transfer matrix, section in Jan Smit's book on Lattice Fields theory

[anony]

Hi guys,

Basically I'm working through Jan Smit's book, http://books.google.com/books?id=pFgUFfG7JygC&printsec=frontcover&dq=introduction+to+quantum+fields+on+a+lattice&hl=en&src=bmrr&ei=mabWTOjtMoK4hAfh0eGGBQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDIQ6AEwAA#v=onepage&q&f=false , and I'm struggling to show equations (2.32),(2.33). Would appreciate it if anyone could point me in the right direction.

I have thus far attempted to expand both sides. That is I made the replacements for \hat{p} and \hat{q} in \hat{T} and in the column vectors. But I don't see how I'm supposed to work any of it out? Am I going about this in the wrong way? For example, the top element in the vector \times \hat{T} should be

exp(\frac{-w^{2}}{4}q^{2}) exp(\frac{1}{2}\frac{\partial^{2}}{\partial q^{2}}) exp(-w^{2}\frac{q^{2}}{4}) \times -i \frac{\partial}{\partial q}

and similarly for all the other terms. Is this the right way to go about it?

Thanks in advance

(sorry, i can't immediately see how to include latex?)

EDIT: I was told that for some google books isn't working on that page, so here is a screen shot of just the section I'm struggling with:
http://img836.imageshack.us/img836/8466/probp.jpg

 

[Kevin_Axion]

It's very difficult to see what the equation is, you need to begin with a tex (square bracketed) and end with a /tex (square bracketed.)