Group theory of massless Boson fields

  • U. H. Niederer
Classical Mechanics, Quantum Mechanics, Field Theory, Statistical Mechanics
Part of the Lecture Notes in Physics book series (LNP, volume 50)


Free massless Boson fields are defined as manifestly covariant unitary representations of the Poincaré group for zero mass and integer spin s . The fields are tensors which, in the simplest case, belong to the representationD(s,0) ⊕ D(0,s) of the Lorentz group. They are characterized by wave equations of two types: (i) The symmetry conditions, which impose the requirement that the tensors indeed carry the representation D(s,0) ⊕ D(0,s), and(ii) the unitarity conditions, which turn out to be of the form {im573-1}

In the case s = 2 the field is a 4th rank tensor, the symmetry conditions are the equations of the Riemann curvature tensor in the linearized vacuum theory of gravitation, and the unitarity conditions are the Bianchi identities.


Wave Equation Irreducible Representation Symmetry Condition Bianchi Identity Unitarity Condition 


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  1. [1]
    U. Niederer, L. O'Raifeartaigh, Fortschritte der Physik 22, 131 (1974)Google Scholar
  2. [2]
    U. Niederer, Group theory of the massless spin 2 field and gravitation, to appear in GRG-Journal.-*** DIRECT SUPPORT *** A3418042 00021Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • U. H. Niederer
    • 1
  1. 1.Institut für Theoretische Physik der Universität ZürichZurichSwitzerland

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