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  • 1980-1984  (698)
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We show that a certain four-dimensional field theory has powerful structures in common with the two-dimensional 0(1, 3) non-linear σ-model.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 72 (1980), S. 119-130 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The constellation concept is recalled (geometrical description of a ray in a vector space). The groups PO(n+1, ℂ) orP Sp(n+1, ℂ) are shown to preserve “harmonic conjugation” between two constellations. The action of the Lorentz subgroup and its rotation subgroup is described. Finally, a theorem concerning Clebsch-Gordan product of constellations is proved.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 72 (1980), S. 131-174 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An existence theorem is proved for a probability measure on continuous paths in space, proposed by Edwards as a stochastic model for the geometric properties of long polymer chains.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 72 (1980), S. 175-205 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The notion of Feynman amplitude associated with a graphG in perturbative quantum field theory admits a generalized version in which each vertexv ofG is associated with ageneral (non-perturbative)n v-point functionH n v,n v denoting the number of lines which are incident tov inG. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle'sG-convolution procedure. In the present work we propose a generalization ofG-convolution which includes the case when the functionsH n v arenot integrable at infinity but belong to a suitable class of slowly increasing functions. A “finite part” of theG-convolution integral is then defined through an algorithm which closely follows Zimmermann's renormalization scheme. In this work, we only treat the case of “Euclidean”r-momentum configurations. The first part which is presented here contains together with a general introduction, the necessary mathematical material of this work, i.e., Sect. 1 and appendices A and B. The second part, which will be published in a further issue, will contain the Sects. 2, 3 and 4 which are devoted to the statement and to the proof of the main result, i.e., the convergence of the renormalizedG-convolution product. The table of references will be given in both parts.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract SupposeU is an open bounded subset of 3-space such that the boundary ofU has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solutionu to the time dependent Navier-Stokes equations of incompressible fluid flow inU such that the curl ofu is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 76 (1980), S. 269-276 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The families of Gibbs semigroups with generators from conveniently bounded monotonous families of self-adjoint operators are proved to be compact in the trace-norm topology.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the dynamics of a quantum mechanical system which consists of some particles with large masses and some particles with small masses. As we increase the large masses to infinity we obtain the following results: The particles of smaller mass move adiabatically and determine an effective potential in which the heavier particles move semiclassically. Our methods can be applied to diatomic molecules with Coulomb forces.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The renormalization group technique is used to study rigorously the λ(∇φ)4 perturbation of the massless lattice field φ in dimensionsd≧2. Asymptoticity of the perturbation expansion in powers of λ is established for the free energy density. This is achieved by using Kadanoff's block spin transformation successively to integrate out high momentum degrees of freedom and by applying ideas previously used by Gallavotti and Balaban in the context of the ultraviolet problems. The method works for arbitrary semibounded polynomials in ∇φ and △φ.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We solve explicitly and without approximation the problem of a quantum-mechanical particle inR 3 subjected to point interactions that are periodic inR 3 with periodicity of the typeZ, Z 2, andZ 3. In the first case we get a model of an infinite straight polymer, in the second case we get a model of a monomolecular layer and in the third case we get a model of a crystal. In all three cases the unit cell of the Bravais lattice is allowed to contain any finite number of interaction sites (atomes), placed arbitrarily and with arbitrary interaction strength. In the case: one interaction site per unit cell we find explicit formulas for the resonance bands and energy bands and their corresponding wavefunctions.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 77 (1980), S. 149-172 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider a nonlinear, elliptic, free-boundary problem involving an initially unknown setA that represents, for example, the cross-section of a steady vortex ring or of a confined plasma in equilibrium. The solutions are characterized by a variational principle which allows us to describe their behaviour under a limiting process such that the diameter ofA tends to zero, while the solutions degenerate to the solution of a related linear problem. This limiting solution is the sum of the Green function of the linear operator and of a smooth function satisfying the boundary conditions. Mathematically speaking, this limiting process, that we call “nonlinear desingularization”, is a novel kind of bifurcation phenomenon since the nonlinear effect here involves smoothing the singularity of the associated linear problem.
    Type of Medium: Electronic Resource
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