creation operators. Similarly in the Ramond sector the expansions are && (z) = ( -i )\^[1/2]{} \_[n]{} a\_[n]{}e\^[i(x+iy)n]{} ,\
&& |(z) = ( i )\^[1/2]{} \_[n]{} |a\_[n]{}e\^[-i(x-iy)n]{} where the zero modes satisfy a\_[0]{}\^2 = , |a\_[0]{}\^2 = . We choose conventions in which the zero modes act on the spin and disorder primary states according to a\_[0]{}|= | , |a\_[0]{}|= -| . The physical state space ${\cal H}_{0}$ is spanned by the states |a\_[k\_1]{}\^…|a\_[k\_p]{}\^a\_[k\_[p+1]{}]{}\^…a\_[k\_N]{}\^|0 , k\_[i]{}1/2 + [Z]{} , N - in the NS sector and by the states |a\_[n\_1]{}\^…|a\^\_[n\_q]{}a\^\_[n\_[q+1]{}]{}…a\_[n\_M]{}\^| , n\_[i]{}, , M - in the R sector. Above $|0\rangle$ stands for the conformal vacuum state.

The Bogolyubov transformation relating the massive and massless theories is \[BogNS1\] b\_[k]{}\^ = f(k){

[l@l]{} (|a\^\_[k]{} - i a\_[k]{}) , k&gt;0\
(a\_[-k]{}\^ + i |a\_[-k]{} ) , k&lt;0

. in the NS sector and \[BogR1\] b\_[n]{}\^ = f(n){

[l@l]{} (|a\^\_[n]{} - i a\_[n]{}) , n&gt;0\
(a\_[-n]{}\^ + i |a\_[-n]{} ) , n&lt;0

. \[BogR2\] b\_[0]{}\^ = {

[l@l]{} ( a\_[0]{} + i|a\_[0]{}) , m&gt;0\
(a\_[0]{} - i|a\_[0]{} ) , m&lt;0

. , b\_[0]{} = {

[l@l]{} ( a\_[0]{} - i|a\_[0]{}) , m&gt;0\
(a\_[0]{} + i|a\_[0]{} ) , m&lt;0

. in the R-sector. In 