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  • 1975-1979  (6)
  • 1965-1969  (6)
Document type
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Yukawa coupling of quantum fields in two dimensions. I (1967)
    Springer
    Communications in mathematical physics 5 (1967), S. 343-386 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A renormalization procedure is proposed. It gives rigorous mathematical meaning to the infinite cancellations in this model. A space cutoff is introduced in the interaction termV and soV has the form $$\int\limits_{\left| x \right| \leqq K} {V\left( x \right)} dx$$ , but there are no momentum cutoffs inV. There is an infinite constant and an infinite boson mass renormalization in this model. The main result is that the renormalized Hamiltonian is rigorously defined as a bilinear form in the Fock Hilbert space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646449
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Particles and scaling for lattice fields and Ising models (1976)
    Springer
    Communications in mathematical physics 51 (1976), S. 1-13 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The conjectured inequality γ(6)≦0 leads to the existence of ϕ d 4 fields and the scaling (continuum) limit ford-dimensional Ising models. Assuming γ(6)≦0 and Lorentz covariance of this construction, we show that ford≧6 these ϕ d 4 fields are free fields unless the field strength renormalizationZ −1 diverges. Let λ be the bare charge and ε the lattice spacing. Under the same assumptions (γ(6)≦0, Lorentz covariance andd≧6) we show that if λε4−d is bounded as ε→0, thenZ −1 is bounded and the limit field is free.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609048
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A note on reflection positivity (1979)
    Springer
    Letters in mathematical physics 3 (1979), S. 377-378 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We establish reflection positivity of covariance operators, using properties of Dirichlet or Neumann boundary data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00397210
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Boson fields with the :Φ4: Interaction in three dimensions (1968)
    Springer
    Communications in mathematical physics 10 (1968), S. 1-47 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The :Φ4: interaction for boson fields is considered in three dimensional space time. A space cutoff is included in the interaction term. The main result is that the renormalized HamiltonianH ren is a densely defined symmetric operator. In addition to the infinite vacuum energy and infinite mass renormalizations, this theory has an infinite wave function renormalization. Consequently the Hilbert space (of physical particles) in whichH ren acts is disjoint from the bare particle Fock Hilbert space in which the unrenormalized Hamiltonian is defined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01654131
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Phase transitions for φ 2 4 quantum fields (1975)
    Springer
    Communications in mathematical physics 45 (1975), S. 203-216 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Phase transitions for the quantum field interaction λφ4+m 0 2 φ2,m 0 2 /λ≪1 are established in two dimensional space time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01608328
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Instantons in aU(1) lattice gauge theory: A Coulomb dipole gas (1977)
    Springer
    Communications in mathematical physics 56 (1977), S. 195-212 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the decompositionA=A I +A SW of aU(1) lattice gauge field into instanton and spin wave parts. The action also decomposes,A=A I +A SW +R. HereA I is a Coulomb dipole gas,A SW is a zero mass free field, andR is a higher order remainder. We studyA I in detail, ford≧4, in the dilute gas case (which corresponds to the low temperature limit of the gauge field theory). We establish the leading behavior of the free energy:f ∼ ɛ−d aζ. Here ɛ is the lattice spacing,a is a geometrical constant and ζ is an activity defined in terms of a small number of instanton configurations. Our methods suggest the absence of screening in the dilute dipole gas,d≧4, in contrast to Debye screening for the dilute monopole gas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01614208
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  • 7
    Electronic Resource
    Electronic Resource
    The Yukawa coupling of quantum fields in two dimensions. II (1967)
    Springer
    Communications in mathematical physics 6 (1967), S. 61-76 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Yukawa coupling in two dimensional space time is considered. A space outoff is introduced in the interaction termV, so that the renormalized HamiltonianH ren is a rigorously defined bilinear form in the Fock Hilbert space. The main result is thatH ren is positive provided the finite part of the renormalization terms are suitably chosen. As a consequence, the Schrödinger equation (i∂/∂t−H ren)Φ=0 can be solved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646323
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    The Schrödinger equation for quantum fields with nonlinear nonlocal scattering (1966)
    Springer
    Communications in mathematical physics 2 (1966), S. 271-300 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper considers perturbationsH=H 0+εV of the Hamiltonian operatorH 0 of a free scalar Boson field.V is a polynomial in the annihilation creation operators. Terms of any order are allowed inV, but point interactions, such as ∫:0(x)4(x)4:dx, are not considered. Unnormalized solutions for the Schrödinger equation are found. For ε→0, these solutions have a partial asymptotic expansion in powers of ε. The set of all possible pertubation termsV forms a Lie algebra. General properties of this Lie algebra are investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01773357
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Two and three body equations in quantum field models (1975)
    Springer
    Communications in mathematical physics 44 (1975), S. 293-320 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In each pure phase of a ℘(φ)2 quantum field model, we establish local regularity of the Green's functions and exponential decay for noncritical models. We establish the existence of two-particle and three-particle Bethe-Salpeter kernels in the Euclidean region.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609832
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  • 10
    Electronic Resource
    Electronic Resource
    The resummation of one particle lines (1979)
    Springer
    Communications in mathematical physics 67 (1979), S. 267-293 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We propose a partial resummation for a weak coupling cluster expansion. The resummation gives one particle lines with in/out field propagators. We give a Bethe-Salpeter equation in which one particle subtractions are defined using physical one particle states. By these methods, we show thatP(φ)2 quantum fields in the weak coupling region have only isolated bound state spectrum below the 2m threshold. HereP is not restricted to be even.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238849
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    Paper (German National Licenses)
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