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  • 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
    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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  • 3
    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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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Boson fields with nonlinear selfinteraction in two dimensions (1968)
    Springer
    Communications in mathematical physics 8 (1968), S. 12-25 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Semiboundedness of the total Hamiltonian is proved for a selfinteracting Boson field in two dimensional space time. The interaction is given by a Wick polynomial:P(Φ):. The polynomialP is required to have even degree and its leading coefficient must be positive. A space cutoff is introduced in the interaction Hamiltonian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646421
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    A Yukawa interaction in infinite volume (1968)
    Springer
    Communications in mathematical physics 11 (1968), S. 9-18 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove the existence of the Heisenberg picture field operators for quantum fields with a Yukawa interaction. The interaction density $$g:\Psi ^ + (x) \Psi (x) \Phi (x):$$ has a momentum cutoff on the Fermions, but no spatial form factor, and is thus translation invariant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01654299
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    Paper (German National Licenses)
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