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:''"FW transformation" redirects to here.'' The Foldy–Wouthuysen transform is widely used in high energy physics. It was historically formulated by Leslie Lawrance Foldy and Siegfried Adolf Wouthuysen in 1949 to understand the nonrelativistic limit of the Dirac equation, the equation for the spin-1/2 particles.〔Foldy, L. L. and Wouthuysen, S. A. (1950). (On the Dirac Theory of Spin 1/2 Particles and its Non-Relativistic Limit ). Physical Review, 78, 29-36.〕〔Foldy, L. L. (1952). The Electromagnetic Properties of the Dirac Particles. Physical Review, 87, (5), 682-693.〕〔Pryce, M. H. L. (1948). The mass-centre in the restricted theory of relativity and its connexion with the quantum theory of elementary particles. Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, A195, 62-81.〕〔Tani, S. (1951). Connection between particle models and field theories. I. The case spin 1/2. Progress of Theoretical Physics, 6, 267-285.〕 A detailed general discussion of the Foldy–Wouthuysen-type transformations in particle interpretation of relativistic wave equations is in Acharya and Sudarshan (1960).〔Acharya, R., and Sudarshan, E. C. G. (1960). Front Description in Relativistic Quantum Mechanics. Journal of Mathematical Physics, 1, 532-536.〕 ==A canonical transform== Foldy and Wouthuysen made use of a canonical transform that has now come to be known as the ''Foldy–Wouthuysen transformation''. A brief account of the history of the transformation is to be found in the obituaries of Foldy and Wouthuysen〔Brown, R. W., Krauss, L. M., and Taylor, P. L. (2001). Obituary of Leslie Lawrence Foldy. Physics Today, 54 (12), 75.〕 〔Leopold, H. (1997). Obituary of Siegfried A Wouthuysen. Physics Today, 50, (11), 89.〕 and the biographical memoir of Foldy. 〔Foldy, L. L. (2006). Origins of the FW Transformation: A Memoir, Appendix G, pp. 347-351 in ''Physics at a Research University'', Case Western Reserve University 1830-1990, () Ed. William Fickinger.〕 Before their work, there was some difficulty in understanding and gathering all the interaction terms of a given order, such as those for a Dirac particle immersed in an external field. With their procedure the physical interpretation of the terms was clear, and it became possible to apply their work in a systematic way to a number of problems that had previously defied solution.〔Bjorken, J. D., and Drell, S. D. (1964). Relativistic Quantum Mechanics. McGraw-Hill, New York, San Francisco.〕〔Costella, J. P., and McKellar, B. H. J. (1995). The Foldy-Woutuysen transformation. ().〕 The Foldy–Wouthuysen transform was extended to the physically important cases of the spin-0 and the spin-1 particles,〔Case, K. M. (1954). Some generalizations of the Foldy–Wouthuysen transformation. Physical Review, 95, 1323-1328.〕 and even generalized to the case of arbitrary spins.〔Jayaraman, J. (1975). A note on the recent Foldy–Wouthuysen transformations for particles of arbitrary spin. J. Phys. A: Math. Gen., 8, L1-L4.〕 The Foldy–Wouthuysen (FW) transformation (after Lesley L. Foldy and Siegfried A. Wouthuysen) is a unitary transformation on a fermion wave function of the form: where the unitary operator is the 4 × 4 matrix: Above, is the unit vector oriented in the direction of the fermion momentum. The above are related to the Dirac matrices by ''β'' = ''γ''0 and ''αi'' = ''γ''0''γ''''i'', with ''i'' = 1, 2, 3. A straightforward series expansion applying the commutativity properties of the Dirac matrices demonstrates that () above is true. The inverse : so it is clear that ''U''−1''U'' = ''I'', where ''I'' is a 4 × 4 identity matrix. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Foldy–Wouthuysen transformation」の詳細全文を読む スポンサード リンク
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