International Journal of Theoretical Physics

, Volume 36, Issue 12, pp 2783–2826 | Cite as

Realizations of causal manifolds by quantum fields

  • Heinrich Saller


Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e., by the homogenous spacesD(n)=GL(C R n )/U(n) withn=1 for mechanics andn=2 for relativistic fields. The rankn gives the number of both the discrete and continuous invariants used in the harmonic analysis, i.e., two characteristic masses in the relativistic case. ‘Canonical’ field theories with the familiar divergencies are inappropriate realizations of the real 4-dimensional causal manifoldD(2). Faithful timespace realizations do not lead to divergencies. In general they are reducible, but nondecomposable—in addition to representations with eigenvectors (states, particle), they incorporate principal vectors without a particle (eigenvector) basis as exemplified by the Coulomb field.


Manifold Irreducible Representation Cartan Subgroup External Group Linear Field 
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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Heinrich Saller
    • 1
  1. 1.Max-Planck-Institut für Physik und AstrophysikWerner-Heisenberg-Institut für PhysikMunichGermany

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