A quantum mechanical theory of local observables and local operations

Local operators are characterized mathematically by means of projection operators on the Banach space of bounded operators. The idea of microlocality, as opposed to macrolocality, is implemented into the theory so as to enable us to define operations that are strictly local. Necessary and sufficient conditions are investigated in order that the interaction of a local measurement instrument with a local quantum field is such a strictly local (or microlocal) operation. Application of the theory to quantum electrodynamics reveals that this theory violates microlocality as defined here. Implications which our theory may have on the issue of quantum nonlocality as studied in relation to the Bell inequalities are discussed.