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Grassmann-Cartan algebra and Klein-Gordon equations

  • The Loyola Conference
  • Papers Presented at the Second New Orleans Conference of Quantum Theory and Gravitation, Loyola University, New Orleans, May, 1983
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Abstract

Given a Riemannian structure (M, g), a hypothesis is investigated that ifα=⊕ n p=0 α p ∈Λ(M) is submitted to the differential condition (g+δ+κ)α=0, κ=mc/ħ—which implies that each component of α fulfills the Klein-Gordon equation (Δ-κ 2)α p =0, α ought to be interpreted as a natural complex of the bosonic fields. Then it is found that the complex α admits the interpretation in the sense of first quantization with Λ(M) being a convex set of states, with the structure of a Hilbert space over ℛ. The definite spin states of bosons are then pure states which are not conserved by the temporal evolution.

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Author notes

  1. Jerzy F. Plebański

    Present address: University of Warsaw, Warsaw, Poland

Authors and Affiliations

  1. Centro de Investigacion y Estudios Avanzados, del I.P.N., AP14-740, Mexico 14, D. F., Mexico

    Jerzy F. Plebański

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  1. Jerzy F. Plebański
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Plebański, J.F. Grassmann-Cartan algebra and Klein-Gordon equations. Int J Theor Phys 23, 895–928 (1984). https://doi.org/10.1007/BF02214073

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  • DOI: https://doi.org/10.1007/BF02214073

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