Abstract |
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The ultimate limit for the smallest measurable distance should be considered as an unknown quantity, whose value /b a/ could be finite as well as zero. This implies that the usual concept of a space-time continuum has to be replaced by the concept of a space-time lattice, and that all field amplitudes can only be defined on the corresponding lattice points. It is shown that a natural extension of the usual theory of /b field/ /b quantization/ leads then to a generalized `energy addition law'. This law reduces to the usual one only when /b a/=0 or when the energies are much smaller than h /b c///b a/. But it corresponds exactly to the energy addition law which is needed in order to preserve the relativistic invariance of the theory. Besides the previously considered generalizations of the Schrodinger, Gordon-Klein and Dirac equations, it is also possible to set up a corresponding generalization of /b Maxwell/'/b s/ /b equations/. Finally it is shown that the (pseudo-) Hamiltonian density of a field can only be subject to an /b equation/ /b of/ /b continuity/ when the fields are varying sufficiently slowly. |