Geodesic
Selfadjointness of some representations of field algebra
Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 1, pp. 9-18

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Essential selfadjointness is proved for the field algebra representations corresponding to the generalized free field and the field ${:}\varphi^2{:}(x)$, where $\varphi(x)$ is a free field. 
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     author = {N. V. Borisov and A. N. Vasil'ev},
     title = {Selfadjointness of some representations of field algebra},
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N. V. Borisov; A. N. Vasil'ev. Selfadjointness of some representations of field algebra. Teoretičeskaâ i matematičeskaâ fizika, Tome 11 (1972) no. 1, pp. 9-18. http://geodesic.mathdoc.fr/item/TMF_1972_11_1_a1/