Summary
(*). — A detailed analysis is made of the theoretical possibilities of constructing a quantum mechanics and consequently of a description of the elementary particles, based on a definition of the postulates of relativistic invariance and then on the simmetry properties connected with the complete Lorentz group, including displacements in space and time and inversions of both the space and the time coordinates. It is then pointed out how the validity of every conclusion deriving from simmetry considerations depends essentially from the fundamental problem of the a «measurability» of the field quantities.
Paper presented at the International Conference on Elementary Particles held at Pisa, June 1955.
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Reference
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These equations are contained already in the articles of reference (3).
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It is contained in various publications such as reference (13) and V. Bargmann and E. P. Wigner: Proc. Nat. Acad. Sc.,34, 211 (1948); E. Inonu and E. P. Wigner:Nuovo Cimento,9, 719 (1952); R. Haag: reference (15).
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This was recognized already by P.A.M. Dirac: Proc. Roy. Soc., 114, 243(1927). Cf. also T. D. Newton and E. P. Wigner:Rev. Mod. Phys., 21, 400 (1949).
This point is indicated also by H. Umezawa, S. Kameiuchi and S. Tanaka:Frog. Theor. Phys, 12, 383 (1955). The same result was obtained by the present writer on the basis of the consideration.of time displacements and the positive nature of the energy(Giittinger Nachr), 1932, p. 546 ).
See reference (13). It should be noted, however, that the time inversion considered there is Pauli’s unitary operator (cf.Rev. Mod. Phys.,13, 203 (1941)).
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Some results for the angular distribution and polarisation were obtained already by C. L. Critchfield and E. Teller:Phys. Rev., 60, 10 (1941); D. R. Hamilton:.Phys. Rev., 71, 546 (1947); E. Eisner and R. G. Sacns:Phys. Rev., 72, 680 (1947); L. Wolfenstein and R. G. Sacns:Phys. Rev., 73, 528-(1948); C. N. Yang:Phys. Rev., 74, 764 (1948).
My indebtedness is particularly great to Drs. V. Bargmann and A. S.
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Wigner, E.P. (1997). Relativistic Invariance in Quantum Mechanics. In: Wightman, A.S. (eds) Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics. The Scientific Papers, vol A / 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09203-3_12
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