Maestretto and Linden 



(H*) = J , , <A(e)A*(e)) 



(2irkr)Vl - M^ sin" 9 



where 



k(x'.x)/ cose ,A 



A(e)A (9)) =\ dx\ dx'e "^ ^ <W{x')W (x) 



and where 



'0 ^'o 



(W(x')W*{x) = ^^ < W^W*) <P„(x')<p,(x) 



m n 



Let Ujj denote the unitary matrix which diagonalizes ( Wf^Wp) , 

 i.e. , the transformation to the actual degrees of freedom. Further, 

 let X-m denote the power in the m^^ degree of freedom, then we have 



<W(x')W*(x)> = 2 <Pi(x')U^iXi5iiUn%n(x) 

 i,j,m,n 



The integrals have already been encountered, they are simply the 

 finite Fourier transform of the <pj^{^) so that, 



<A(9)A*(9)) = 2, ^i(z)U^i>^iSijUn%j(-z) 



where 



z = 



i,j,m/i 



,, cos 9 T. , 



ik A q - ^ 



yi - M^ sin^ 9 



M^ - 1 



508 



