Notes on Dirac's New Quantization Method in the Field Theory

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universal validity for all kinds of wave fields accessible at present since, for example, the renormalization of an electric charge closely associated with the vacuum polarization has been shown to be entirely invalid in the vector meson theory4). Recently, Dirac's new methodS) of field quantization associated with the introduction of negative energy photon has been proposed with some success to remove the divergency of mass term in one electron theory. Although his theory has entirely failed to eliminate the mentioned divergency in the hole theory together with the . inclusion of another difficulty concerning the physical interpretation of negative probability, it seems to provide us a provisional but attractive footing for the future developnlent of the field theory since it is based on the quite natural generalization of the metric in Hilbert space upon which the mathematical scheme of the ordinary quantum mechanics has been formulated in a consistent way. In fact, if Pauli's qualitative consideration of Dirac's theory mentioned above were actually correct, the self-energy, to any degree of order, of an electron would be brought to vanish in one electron problem6), which fact seems to draw much attention in view of the present situation that the provi­ sional theories proposed so far are almost restricted merely to the second order self-energy. After all, since the merit or demerit of Dirac's new method of field quantization should be eventually criticized only through its application to the various kinds of physical phenomena in a close connection with the experimental results, we have here worked out the fourth order self-energy of a free electron and the Lamb-shift, i.e., the second order radiative reaction of a bound electron in hydrogen atom in order to provide a useful data for judging the physical

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