Abstract
Here we want to outline briefly how to construct wave functions which describe particles with spin s = 1, 3/2... out of solutions of the Dirac equation and also to study by what kind of wave equation they are generated. As already seen in Chap. 6, the lower components of free solutions of the Dirac equation with positive energy vanish in the case m 0 ≠ 0 in the rest system of the particles [cf. (6.13)]. Thus, for E p = m 0 c 2 (which means p i- = 0 when we are in the rest system) the spinor components are given by W (r)α (0) = δrα and thus
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Biographical Notes
BARGMANN, Valentine, *April 6, 1908 in Berlin, wrote phD thesis in Zürich (1936), Associate Professor of Mathematics in Pittsburgh (1948) and, since 1957, Professor in Princeton. Main fields of activity: quantum theory, theory of relativity and group theory.
WEYL, Claus Hugo Hermann, mathematician, *9.11.1885 Elmshorn (Germany), †9.12.1955, Zürich. W. was appointed as professor in 1913 at ETH Zürich, in 1930 at Göttingen and then in 1933 at Princeton. W. worked on the theory of differential and integral equations and later connected topological considerations with the conceptions of Riemannian surfaces. Meeting with A. Einstein inspired him to his fundamental publication Raum, Zeit, Materie [Space-Time-Matter (Dover 1950)], which contains a chapter where he tries to unify gravitation and electromagnetism. This is considered by many as the first approach to what we call nowadays gauge theories. For the representation of mathematical groups used in quantum mechanics he developed an integral method, contrary to the infinitesimal methods of S. Lie and E. Cartan. W. stood for intuitionism (a method for a constructive foundation of mathematics) and tried to maintain a close connection between mathematics, physics and philosophy in his own work.
KEMMER, Nicholas, British theoretical physicist, *7.12.1911, St. Petersburg (now Leningrad), trained at the Bismarckschule in Hannover as well as at the universities in Göttingen and Zürich; he took up the appointment of professor of mathematical physics in Edinburgh in 1953, in 1979 becoming emeritus professor. 1983 he was awarded the Max Planck medal of the German Physical Society.
SCHWINGER, Julian Seymour, * 12.03.1918, New York, Professor at Harvard University and California University, contributed fundamentals to QED, discovered charge and mass renormalization, with the aid of which he calculated the Lamb-shift. For this ge got, together with R. Feynman and S. Tomonaga the Noble Prize in Physics in 1965. Moreover he worked on quantum field theory, many-body problems, etc.
FIERZ, Markus, * 1912, Basel, assistent to W. Pauli, 1944–60 professor at the university of Basel, from 1960 professor at ETH Zürich, 1959 director of the Theoretical Division at Cern. He made various fundamental contributions to theoretical physics, e.g. the “Fierz-transformations” (see Vol.5 of this series).
GUPTA, Suraj Narayan, * 1.12.1924, Haryana (India), professor at the Wayne state university (since 1956). Main fields of research: theory of relativity, gravitation, quantum electrodynamics, nuclear physics, highenergy physics.
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© 1990 Springer-Verlag Berlin Heidelberg
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Greiner, W. (1990). Wave Equations for Particles with Arbitrary Spins. In: Relativistic Quantum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02634-2_15
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DOI: https://doi.org/10.1007/978-3-662-02634-2_15
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