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On the concept of conformal invariance for a free particle

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Lettere al Nuovo Cimento (1971-1985)

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  1. We adopt the diagonal metric tensorg μν=g μν withg 00=−g 11=−g 22=−g 33=1, and setɛ 0123 = − 1. In the finite-dimensional representation {m, n} ofSL 2,C , where 2m and 2n are nonnegative integers, the generatorss μν=−s νμ satisfy 1/2s μν s μν=m(m+1)+n(n+1), and (i/8)ɛ μνϱσ s μν s ϱσ =m(m + 1) −n(n + 1).

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  5. Such operators might be obtained in the usual way, by integration from corresponding conserved currents. The latter are discussed in ref. (3);J. S. Lomont:Nuovo Cimento,22, 673 (1961);L. Gross:Journ. Math. Phys.,5, 687 (1964).

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  8. This is in fact the componentA=C=0 of the identity (m AB m BC +m CB m BA )ψ = 2(1 −λ 2)g A C ψ, which is known to characterize the corresponding ladder representation ofSU 2,2. SeeA. O. Barut andA. Böhm:Journ. Math. Phys.,11, 2938 (1970).

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  1. Department of Mathematical Physics, University of Adelaide, Adelaide, S. A.

    A. J. Bracken (Rothmans Fellow)

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  1. A. J. Bracken
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Bracken, A.J. On the concept of conformal invariance for a free particle. Lett. Nuovo Cimento 7, 321–324 (1973). https://doi.org/10.1007/BF02725978

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