Abstract
The two-component spinor theory of van der Waerden is put into a convenient matrix notation. The mathematical relations among various types of matrices and the rule for forming covariant expressions are developed. Relativistic equations of classical mechanics and electricity and magnetism are expressed in this notation. In this formulation the distinction between time and space coordinates in the four-dimensional space-time continuum falls out naturally from the assumption that a four-vector is represented by a Hermitian matrix. The indefinite metric of tensor analysis is a derived result rather than an arbitrary ad hoc assumption. The relation to four-component spinor theory is also discussed.
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References
B. L. van der Waerden,Nachr. Akad. Wiss. Göttingen, Math.-Physik, K. 100 (1929);Die Gruppentheoretische Methode in der Quantenmechanik (Berlin, Springer, 1932).
W. L. Bade and H. Jehle,Rev. Mod. Phys. 25, 714 (1953); W. C. Parke and H. Jehle, inLectures in Theoretical Physics (University of Colorado Press, Boulder, 1965), Vol. VIIA, p. 297.
T. D. Lee and C. N. Yang,Phys. Rev. 105, 1671 (1957).
L. M. Brown,Phys. Rev. 111, 957 (1958); inLectures in Theoretical Physics, ed. by W. E. Brittin, B. W. Downs, and J. Downs (University of Colorado Press, Boulder, 1962), Vol. IV, pp. 324–357.
E. Marx,Physica 49, 469 (1970).
R. F. Streator and A. S. Wightman,PCT, Spin and Statistics, and All That (Benjamin, New York, 1964), p. 12.
F. Gürsey,Nuovo Cimento 3, 988 (1956).
O. Laporte and G. E. Uhlenbeck,Phys. Rev. 37, 1370 (1931).
A. Messiah,Quantum Mechanics (North-Holland, Amsterdam, 1962), Vol. II, p. 896.
D. Hestenes,Space-Time Algebra (Gordon and Breach, New York, 1966);Am. J. Phys. 39, 1013 (1971).
J. D. Edmonds, Jr.,Am. J. Phys. 42, 220 (1974);Found. Phys. 3, 313 (1973).
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Frost, A.A. Matrix formulation of special relativity in classical mechanics and electromagnetic theory. Found Phys 5, 619–641 (1975). https://doi.org/10.1007/BF00708433
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DOI: https://doi.org/10.1007/BF00708433