Annali di Matematica Pura ed Applicata

, Volume 89, Issue 1, pp 363–379 | Cite as

Construction of representations of the Poincaré Lie algebra by extension of direct integrals of representations ofSL(2,C)

  • Vittorio Cantoni


As a first application of a general method of construction, a class of representations of the Lie algebra
of the Poincaré group
, which includes Wigner’s representations with spin zero and positive mass, is obtained by forming suitable direct integrals of representations of class I of the principal series of SL(2, C) and extending them to
by means of four additional momentum operators which are determined in explicit form.


Direct Integral 
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Copyright information

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • Vittorio Cantoni
    • 1
  1. 1.Roma

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