
It is investigated to what extent conservation laws are satisfied in non-loeal field theories. First it is shown that from the invariance of the action integral with respect to gauge transformations of the first kind, translations and rotations of space-time there follow the integral conservation laws. These integral laws express that certain functionals of a space-like surface Σ have equal values at the boundaries Σ1 and Σ2 of the domain of space-time considered in the problem. These functionals have the disadvantage of being not constant in the region between Σ1 and Σ2. Another disadvantage is, that they do not correspond with the local charge, momentum and angular momentum. It is shown further, that starting with the Euler-Lagrange field equations it is possible to construct other functionals of Σ being constant throughout the region (Σ1,Σ2) and satisfying at the same time the correspondence principle. These functionals may, therefore, be interpreted as the total charge, momentum and angular momentum of the non-local system. The integral conservation laws follow from the differential laws if the condition of invariance with respect to the three above types of transformations is satisfied. The general considerations are illustrated on a simple example of a non-local field theory.
quantum theory
quantum theory
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