Frve Classes of Transformations of Dirac Spinors : The free-particle Dirac equation is brought to "p_0-,"p_1-"p_2-,"p_3- and "m-linear" forms

概要

論文の詳細を見る
The free-particle Dirac equation has two remarkable features: (1) It is linear in all four components of the energy-momentum p_μ, and also in the mass m. (2) For its solutions there are five distinct simple modes of the invariant scalar product in the momentum representation. In this paper, a theorem presented by Case is generalized and used to obtain five classes of transformations of the Dirac equation. Every transformation in a given class has two properties characteristic of the class: (1) The linearity in a corresponding one of the five quantities p_μ, m is maintained in the transformed equation. (In this way "p_0-,"p_1-"p_2-,"p_3- and "m-linear" forms of the Dirac equation are obtained.) (2) A corresponding mode of the invariant scalar product is preserved. Thus all five classes consist of canonical transformations. Included amongst the "p_0-linear" forms are the Foldy-Wouthuysen-Tani equation, and the one commonly attributed to Cini and Touschek, together with equations appropriate to limiting situations other than the non-relativistic and extreme relativistic ones. The "canonical" form proposed by Chakrabarti is of the "m-linear" type. Belonging to all three of the "p_1-,"p_2- and "p_3-linear" categories is a "P-linear" form of significance for large |P|.
理論物理学刊行会の論文
1969-03-25