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  • 1970-1974  (533)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The technique of phase plane analysis, which was used in a previous paper [4] to study the behaviour of a class of perfect-fluid anisotropic cosmological models, is applied to some simple anisotropic models that contain a uniform magnetic field. A formal correspondence is established between these magnetic models (of Bianchi type I) and certain perfect fluid models (of Bianchi type II), and new exact solutions are consequently discovered.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract InvariantSU(3) octet tensors are constructed in terms of λ matrices and applied to the problem of forming tensors from a single octet used repeatedly. Next a similar problem but with two octets is considered which demonstrates that different outer products of invariant tensors may be related. Finally, a theorem is proved which shows that the number of invariant tensors is essentially finite, and that relations of ranks greater than six exist on outer products of these tensors.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 27 (1972), S. 155-161 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The exact solution of the Dirac equation with a central potential, in the semi-relativistic approximation, is derived and formulae for phase shifts and eigenvalue equations are given.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 27 (1972), S. 166-166 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 27 (1972), S. 181-194 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown how a renormalized perturbation series can be defined for a theory with strictly local, non-polynomial, interacting Lagrangian so as to preserve locality at every order.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 27 (1972), S. 167-180 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In order to construct the quantum field theory in a curved space with no “old” infinities as the curvature tends to zero, the problem of contraction of representations of the corresponding group of motions is studied. The definitions of contraction of a local group and of its representations are given in a coordinate-free manner. The contraction of the principal continuous series of the de Sitter groupsSO 0(n, 1) to positive mass representations of both the Euclidean and Poincaré groups is carried out in detail. It is shown that all positive mass continuous unitary irreducible representations of the resulting groups can be obtained by this method. For the Poincaré groups the contraction procedure yields reducible representations which decompose into two non-equivalent irreducible representations.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 27 (1972), S. 223-234 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that positive linear functionals on the field algebra are necessarily continuous and can be represented by conical measures. Furthermore extension theorems for continuous linear functionals, defined on a subspace of the field algebra, to positive linear functionals are discussed.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 27 (1972), S. 195-222 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract With $$\mathfrak{A}$$ aC*-algebra with unit andg∈G→α g a homomorphic map of a groupG into the automorphism group ofG, the central measureμ Φ of a state Φ of $$\mathfrak{A}$$ is invariant under the action ofG (in the state space of $$\mathfrak{A}$$ ) iff Φ is α-invariant. Furthermore if the pair { $$\mathfrak{A}$$ ,G} is asymptotically abelian, Φ is ergodic iffμ Φ is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on $$\mathfrak{A}$$ , the associated covariant representations of { $$\mathfrak{A}$$ , α} are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 16 (1970), S. 123-135 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We find a Hölder Banach space in which the Bethe-Salpeter equation is a compact integral equation as it stands. We study the properties of the solution in preparation for an analysis of linear field theory models of 3-body amplitudes. In particular we study the properties of the Regge poles of the solution and prove the existence and uniqueness of on mass shell scattering amplitudes.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 16 (1970), S. 105-122 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A certain class of positive functionals on a group algebra is examined that is pertinent to the induced representations of Frobenius and Mackey. Though these functionals are not bounded in theL 1 norm, continuity still persists to an extent that secures the existence of a continuous group representation obtained from Gelfand's construction. The theory thus developed provides a new aspect of both the “improper states” in quantum theory and the induced representations of groups. The method is applied to the Poincaré group and it is shown that the representations, in which particles can be accommodated, are determined up to unitary equivalence by unbounded functionals of a simple structure. It is stressed that representations describing an infinitely degenerate vacuum emerge from mass nonzero representations as the mass tends to zero.
    Type of Medium: Electronic Resource
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