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Prog. Theor. Phys. Vol. 12 No. 2 (1954) pp. 156-166

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On the Construction of Potential in Field Theory

Nobuyuki Fukuda, Katuro Sawada* and Mituo Taketani**

Department of Physics, Tokyo University of Education
*Department of Physics, Tokyo University
**Department of Physics, Rikkyo University

(Received May 12, 1954)

Abstract:

The general formal construction of potential in the field theory is given. It is constructed so as to conserve the normalization of the wave function, irrespective of the switch-off or -on of the potential. The potential is analyzed into its normal part and probability operator. The probability operator is shown to be related to the probability of the system staying in the same state as it does when the interaction is switched off.
From the probability character of the probability operator, we can get a measure of the applicable region of the power series expansion of potential in the coupling constant. The intense meson cloud around the nucleon gives rise to strong singularities in the normal part of the potential, but, on the other hand, the probability of the nucleon to be bare becomes much smaller, and thus it turns out that the actual potential has a lesser singularity. Both potentials derived previously by Taketani-Machida-Ônuma (T.M.O.) and its corrected from by Brueckner-Watson (B.W.) are shown to be two extreme cases in handling this probability operator, but the latter one is more appropriate qualitatively in many cases. The reasonable way of constructing the potential is given in the following paragraphs and the justification of this argument will be illustrated in a separate paper for the pseudo-scalar meson theory.


URL : http://ptp.ipap.jp/link?PTP/12/156/
DOI : 10.1143/PTP.12.156

[ Full Text PDF : FREE ACCESS (929K) ] Citation:

References:

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