Linear relativistic hamiltonians |
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Authors: | Ralph F Guertin Charles G Trahern |
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Institution: | Physics Department, Rice University, Houston, Texas 77001 USA |
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Abstract: | A 2(2J + 1)-component relativistic Hamiltonian H that describes free particles of mass m and spin J is said to be linear if it has the form , where , h is a numerical factor, and g commutes with x and p. All such Hamiltonians are found, provided that the metric is either the unit matrix or ?3 and provided that the theory is invariant under the discrete symmetries. If the operator Γ in the generator of Lorentz boosts is required to be local, there are only two possibilities; either Γ = 0, which generalizes the Dirac spin- theory, or , which generalizes the Sakata-Taketani spin-0 and spin-1 theories. The relationship to linear manifestly covariant equations and its significance is discussed. |
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