Il Nuovo Cimento (1955-1965)

, Volume 26, Issue 5, pp 1066–1089 | Cite as

Generally covariant dirac equation and associated boson fields

  • H. Leutwyler


We reject the equation of the classical formalism of covariant spinor analysis wherein the field of the affine connection in spinor space, γΜ(x), is fixed byDΜγgn= 0. By a closer analogy to tensor analysis in metric space we find only reality conditions imposed on γΜ(x), with considerable independent dynamical freedom remaining. This suggests an approach similar to the procedure of Yang and Mills. Starting with a variational principle we obtain a nonlinear wave equation with non-vanishing rest mass for the affine field γΜ(x), whose structure is dictated by invariance requirements. As particular examples, we discuss Maxwell‘s equations and the pseudoscalar meson-nucleon interaction, in addition to Heisenbergs nonlinear spinor equation.


Si respinge l‘equazione del formalismo classico dell‘analisi degli spinori covarianti in cui il oampo delle oonnessioni affini nello spazio spinoriale, γΜ(x),è fissato da DΜγΝ = 0. Con una più stretta analogia all‘analisi tensoriale nello spazio metrico si troyano solo condizioni di realità imposte a γΜ(x), mentre rimane una considerevole libertà dinamica indipendente. Questo suggerisce un accostamento simile alla procedura di Yang e Mills. Partendo da un principio variazionale si ottiene un‘equazione d‘onda non lineare con massa di quiete che non si annulla per il oampo affine γΜ(x), la cui struttura è imposta dalle esigenze di invarianza. Come esempi particolari, si discutono le equazioni di Maxwell e l‘interazione pseudoscalare mesone-nucleone, oltre all‘equazione spinoriale non lineare di Heisenberg.


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Copyright information

© Società Italiana di Fisica 1962

Authors and Affiliations

  • H. Leutwyler
    • 1
  1. 1.Institut für Theoretische Physik der UniversitÄt BernSwitzerland

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