On the Meaning of the Solution to the One-Body Dirac Equation

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概要

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• In this paper we try to give another demonstration of a theorem concerning a fermion interacting with an external field ; this theorem, which is first shown by Furry, states that in the treatment of the interaction with external fields it is sufficient for one to know the complete set of the solutions to the one-body Dirac equation, even when the fermion field is quantized according to the hole theory for negative energy states. Our demonstration rests on the examination of the effects which are generated by a special type of canonical transformation on the Hamiltonian of the system. But the knowledge of the one-body solution is insufficient to predict the results of the hole theory, when the fermion is interacting with a quantized boson field. By the further examination of the transformation similar to the above, we can find to what extent the one-body solution is efficient in the whole scheme of quantized fields. Using some techniques of the operator calculus, a way is shown by which we can compute exactly, at least formally, the correction terms coming from the effects of the negative energy sea of fermions. The effects of the hole-theoretical vacuum may be classified into two kinds ; one is due to the genuine vacuum polarization which comes into play in our calculation in the form of spur expressions(and is represented by closed loops in Feynman diagrams), and the other is due to the exclusion principle which acts on the negative energy intermediate states(and plays its role in the process represented by connected one-line Feynman diagrams). Formal procedures to compute the latter type of corrections to the one-body solution are explained by the example of nucleon field interacting with neutral pseudoscalar meson field. Four-dimensional aspect of the problem and the invariance to the charge conjugation are also considered.

• 理論物理学刊行会の論文

著者

• Yamazaki Kazuo

  Department Of Anesthesia Kobe Nishi-shimin Hospital

• Yamazaki Kazuo

  Department Of Physics Kyoto University:research Institute For Fundamental Physics Kyoto University

• Tani Smio

  Department Of Industrial Chemistry Kyoto University:department Of Physics Tokyo University Of Educat

• YAMAZAKI Kazuo

  Department of Physics, Kyoto University:Research Institute for Fundamental Physics, Kyoto University

• TANI Smio

  Department of Industrial Chemistry, Kyoto University:Department of Physics, Tokyo University of Education

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