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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 153-175 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The effect of relaxation is important in many physical situations. It is present in the kinetic theory of gases, elasticity with memory, gas flow with thermo-non-equilibrium, water waves, etc. The governing equations often take the form of hyperbolic conservation laws with lower-order terms. In this article, we present and analyze a simple model of hyperbolic conservation laws with relaxation effects. Dynamic subcharacteristics governing the propagation of disturbances over strong wave forms are identified. Stability criteria for diffusion waves, expansion waves and traveling waves are found and justified nonlinearly. Time-asymptotic expansion and the energy method are used in the analysis. For dissipative waves, the expansion is similar in spirit to the Chapman-Enskog expansion in the kinetic theory. For shock waves, however, a different approach is needed.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 213-223 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that expressed in the appropriate principal bundles, the gravitational and Yang-Mills fields equations are equivalent to integrability conditions and that the latter can also be interpreted, using local sections, as conservation equations of the local pseudo-densities of energy-momentum and Yang-Mills charge respectively. These densities can be related using a Kaluza-Klein unification.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 241-255 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract One-dimensional Ising spin systems interacting via a two-body random potential are considered; a decay with the distance like 1/r 1+ε is assumed. We consider only boundary conditions independent of the random realization of the interactions and prove uniqueness and cluster properties of Gibbs states with probability one.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 257-289 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We bound the large order behavior of these pieces of the renormalized perturbation expansion for ρ 4 4 which do not contain “renormalons” [1]. The bound we obtain has the form of the leading asymptotic behavior computed by the Lipatov method, with the exact value of the “Lipatov constant.” Therefore, this paper is a step towards the rigorous study of the large order behavior of Φ 4 4 and towards a proof of existence of the first “renormalon” singularity which should prevent the theory from being Borel summable. Using the results of this paper and the techniques of [15], one can for instance improve [17] the estimate [18] on the finiteness of the radius of convergence of the Borel transform of renormalized Φ 4 4 and obtain that this radius is at least the exact value conjectured in [1].
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 319-352 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Non-local order parameters are constructed in theZ(2) Higgs model to probe the existence or non-existence of charged states. The non-local field corresponding to the Higgs field in a complete gauge fixing is found to be an order parameter for the locally unobservable global gauge symmetry breaking. This symmetry breakdown is shown to imply perfect screening for the bare charge.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 291-318 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The possible ways of compacitification of theE 8 ⊗E 8 Superstring theory to four dimensions are reviewed. The phenomenological need forN=1 supersymmetry is argued (on quite general grounds) to favour the choice of a Calabi-Yau manifold for the compact internal manifold. The massless spectrum after compactification is derived in full detail revealing, beside the usual particles, others that may have great phenomenological impact. The technical aspects of the construction of such manifolds are examined and the methods of calculation of the relevant topological properties are given. A big family of such constructions, giving rise to many new Calabi-Yau manifolds, is presented and its relevance to the search of a phenomenologically acceptable solution is discussed.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 353-361 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that any quantum dynamical semigroup can be written with the help of the solution of a vector-valued classical stochastic differential equation. Moreover this equation leads to a natural construction of a unitary dilation in term of Wiener spaces.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 363-374 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract LetH N be the quantum mechanical Hamiltonian for a neutral system of 2N charged particles, each of unit charge. The HamiltonianH N is assumed to act on wave functions ψ inL 2(ℝ6N ) which satisfy Bose statistics. It is shown that if the kinetic energy of ψ is sufficiently small, then 〈ψ|H N |ψ〉≧−CN 7/5 for some universal constantC.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 391-421 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We determine all the resonances in certain rectangular regions of the complex plane of the Schrödinger operator −h 2Δ+V whenh→0, under the assumption that the set of trapped points of energy 0 for the classical flow form a closed trajectory and that the corresponding Poincaré map is hyperbolic.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 108 (1987), S. 375-389 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The cohomology theory of supermanifolds is developed. Its basic properties are established and simple examples given. The Wess-Zumino term in the Green-Schwarz covariant superstring action is interpreted as a nontrivial class in the “supersymmetric cohomology” of flat superspace. A quotient supermanifold with nontrivial topology reflecting this class is constructed. It is shown that there is no topological quantization condition for the coefficient of the Wess-Zumino term. The superstring differs from conventional sigma models in this respect because its action is Grassmann-valued and its group manifold (superspace) is noncompact.
    Type of Medium: Electronic Resource
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