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  • 1
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The conditions under which a tensor field can be regarded as an energy-momentum tensor are discussed. The problem connected with dilatational and conformal symmetries are exhibited.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Let us consider a quantum theory of one scalar, real, local, Poincaré covariant fieldA(x) with the restricted spectrum condition (massive one particle states and a unique vacuum). The asymptotic fieldsA in out (x) are assumed to be irreducible. Our conjecture is that under some technical assumptions the “charge” of every real, hermitean, locally conserved, Poincaré covariant quantum (pseudo) vector fieldj μ(x) relatively local toA(x), appearing in this theory-vanishes. This means that in a theory of one scalar, real field with a massive particle one can not expect to get symmetry groups induced by conserved (pseudo) vector currents, only by global, selfadjoint, Poincaré invariant generators. Our arguments can be easily extended to a theory of one complex scalar field, in this case the only symmetry transformation induced by a current can be the gauge transformation. We prove also that under very weak assumptions two fields related to each other by a unitary (or similarity) transformation are equal barring some patological cases.
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  • 3
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Let us consider a theory ofn scalar, real, local, Poincaré covariant quantum fields forming an irreducible set and giving rise to one particle states belonging to the same mass different from zero. The vacuum is unique. It is shown under fairly weak assumptions that every Poincaré and TCP invariant symmetry of the theory, implemented unitarily, which mapps localized elements of the field algebra into operators almost local with respect to the former (such a symmetry we call a physical one) can be defined uniquely in terms of the incoming or outgoing fields and ann-dimensional (real) orthogonal matrix. The symmetry commutes with the scattering matrix. Incidentally we show also that the symmetry groups are compact. A special case of these symmetries are the internal symmetries and symmetries induced by locally conserved currents local with respect to the basic fields and transforming under the same representation of the Poincaré group. We may make linear combinations out the original fields resulting in complex fields and its complex conjugate in a suitable way. The inspection of the representations of the groupsSO(n) and their subgroups sheds some light on the s.c. generalized Carruthers Theorem concerning the self- and pair-conjugate multiplets.
    Type of Medium: Electronic Resource
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