A Realistic Model of Convergent Relativistic Quantum Mechanics of Interacting Particles
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概要
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A model of convergent relativistic quantum mechanics of interacting particles in which the particle number is not conserved is obtained. The model somewhat resembles the so-called φ^4 theory, but differs from the latter at the following points. i) It is given in terms of creation and annihilation operators in momentum space representation, and the Hamiltonian does not contain those terms which are products of only creation operators or only annihilation operators like A^†A^†A^†A^† or AAAA. Hence the model is free from the divergence difficulties arising from <0|AAAAA^†A^†A^†A^†|0>. ii) The model incorporates the invariant form factors from the start, and hence is free from the ultraviolet divergence difficulties. iii) The model is obtained as a solution of the fundamental commutator equations for ten generators of the Poincare group. On solving the equations, the primary interaction Hamiltonian which is the sum of the terms A^†A^†A^†A, A^†A^†AA and A^†AAA multiplied by the form factors is used as an input. Thus the model substantially forms a unitary reducible representation of the Poincare group. The S-matrix elements for two-particle elastic scattering and two-particle production processes are calculated up to second order with respect to the coupling constant. The dress-ing effect and the contributions to real processes of the particle-number-changing interaction terms are examined. The implication of these results on the future application of this formal-ism to quantum electrodynamics is mentioned.
- 理論物理学刊行会の論文
- 1973-05-25
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