Note on the Eigenvalue Problem in the Quantum Field Theory
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概要
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In the quantum mechanics of atoms and molecules, many eigenvalue problems are solved in good agreement with experiments. While, in the quantum mechanics of wave fields, the problem is so complicated because of its infinite degrees of freedom that we had to abandon the hope of obtaining the solution. The recent vivid development in the quantum electrodynamics had brought brilliant informations on such problems as scattering, production and capture. These calculations are essentially based on the S matrix formalism^<1)2)>and shows the usefulness of the concept of S matrix, in which it is assumed that the interaction is switched on adiabatically in the remote past and switched off again adiabatically in the remote future. And as its result, the kinetic energy and momentum of the total system is conserved. But in some respect, the use of S matrix in the eigenvalue problem seems to be inadequate, since the truly conserved quantity should be the total energy including the potential(or interaction)energy, but not the mere kinetic energy. This fact seems to show us that the total energy is not an adiabatic invariant, and we should not use the concept of "remote past or future" in the eigenvalue problem. In this short note, we discuss how to formulate the problem, and how the qualitative nature of the eigenvalues will be. And in this problem, it is pointed out that we should always carefully doubt the properties of operators if they are surely hermitian, surely unitary.
- 理論物理学刊行会の論文
著者
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Nishijima Kazuhiko
Department Of Physics Chuo University
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Nishijima Kazuhiko
Department Of Physics University Of City Osaka
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