Abstract: The essential self-adjontness of symmetric fields and the local commutativity of spectral projections is discussed.Local von Neumann rings for any operator from  the Borchers class of the free fields is constructed.The relation between the Borchers-Zimmermann bound and the essential self-adjointness of a symmetric field.

Key words: symmetric field, essential self-adjointness, local commutativity of spectral projection, Borchers-Zimmermann bound