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  • 1
    Electronic Resource
    Electronic Resource
    Euclidean invariant integral representations for Schwinger functionals (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 311-320 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that if the Schwinger functions of a Wightman theory with a mass gap can be represented as moments of a complex measure, there is also such a representation by a measure that is invariant under the Euclidean group. A necessary and sufficient condition is also given for the exponential of a quadratic form on the test function space to be the characteristic functional of a complex measure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527336
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  • 2
    Electronic Resource
    Electronic Resource
    Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions (1994)
    Springer
    Communications in mathematical physics 161 (1994), S. 77-124 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ→∞ in the following three regions:B≪Z 4/3,B≈Z 4/3 andZ 4/3≪B≪Z3. In each case this is accomplished by a modified Thomas-Fermi (TF) type theory. We also analyze these TF theories in detail, one of their consequences being the nonintuitive fact that atoms are spherical (to leading order) despite the leading order change in energy due to theB field. This paper complements and completes our earlier analysis [1], which was primarily devoted to the regionsB≈Z 3 andB≫Z3 in which a semiclassical TF analysis is numerically and conceptually wrong. There are two main mathematical results in this paper, needed for the proof of the exactitude of the TF theories. One is a generalization of the Lieb-Thirring inequality for sums of eigenvalues to include magnetic fields. The second is a semiclassical asymptotic formula for sums of eigenvalues that isuniform in the fieldB.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099414
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  • 3
    Electronic Resource
    Electronic Resource
    On the algebra of test functions for field operators (1973)
    Springer
    Communications in mathematical physics 34 (1973), S. 315-333 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that every continuous linear functional on the field algebra can be defined by a vector in the Hilbert space of some representation of the algebra. The functionals which can be written as a difference of positive ones are characterized. By an example it is shown that a positive functional on a subalgebra does not always have an extension to a positive functional on the whole algebra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646476
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Translationally invariant states and the spectrum ideal in the algebra of test functions for quantum fields (1981)
    Springer
    Communications in mathematical physics 81 (1981), S. 401-418 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A class of states on Borchers' tensor algebra is constructed. These states are invariant under the translation group and fulfill the spectrum condition. This leads to a characterization of the linear span of all such states in terms of a simple continuity property.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01209075
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  • 5
    Electronic Resource
    Electronic Resource
    Zero-mass infinite spin representations of the Poincaré group and quantum field theory (1970)
    Springer
    Communications in mathematical physics 18 (1970), S. 195-203 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that a local quantized field with a manifestly covariant transformation law under the Poincaré group cannot have nonvanishing matrix elements between the vacuum and an irreducible subspace of zero mass and infinite spin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01649432
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Atoms in Strong Magnetic Fields:¶The High Field Limit at Fixed Nuclear Charge (2000)
    Springer
    Communications in mathematical physics 212 (2000), S. 703-724 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: Let E(B,Z,N) denote the ground state energy of an atom with N electrons and nuclear charge Z in a homogeneous magnetic field B. We study the asymptotics of E(B,Z,N) as B→∞ with N and Z fixed but arbitrary. It is shown that the leading term has the form (ln B)2 e(Z,N), where e(Z,N) is the ground state energy of a system of N bosons with delta interactions in one dimension. This extends and refines previously known results for N= 1 on the one hand, and N,Z→∞ with B/Z 3→∞ on the other hand.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200000239
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  • 7
    Electronic Resource
    Electronic Resource
    Local nets and self-adjoint extensions of quantum field operators (1991)
    Springer
    Letters in mathematical physics 21 (1991), S. 151-155 
    Details
    ISSN: 1573-0530
    Keywords: 81E05 ; 47D45 ; 47D40
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider Wightman fields having the property that some closed extensions of the field operators generate locally commuting von Neumann algebras. We show that for such fields the hermitian field operators have self-adjoint extensions, possibly in an enlarged Hilbert space, such that bounded functions of the self-adjoint operators commute locally.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00401649
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  • 8
    Electronic Resource
    Electronic Resource
    Thomas-Fermi theory for matter in a magnetic field as a limit of quantum mechanics (1991)
    Springer
    Letters in mathematical physics 22 (1991), S. 107-117 
    Details
    ISSN: 1573-0530
    Keywords: 81Sxx ; 82C05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The Thomas-Fermi theory for electrons and fixed nuclei in a homogeneous magnetic field is shown to be a limit of quantum mechanics in the following sense: If the nuclear charges and the number of eletrons are multiplied by a, and the magnetic field by a 4/3, then the ground-state energy, divided by a 7/3, converges to the TF energy when a → ∞. A similar result holds also for the electronic density. This generalizes corresponding theorems for zero magnetic field due to Lieb, Simon, and Baumgartner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00405174
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  • 9
    Electronic Resource
    Electronic Resource
    A note on essential duality (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 127-141 
    Details
    ISSN: 1573-0530
    Keywords: 81T05 ; 47D45
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract By considering some simple models, it is shown that the essential duality condition for local nets of von Neumann algebras associated with Wightman fields need not be fulfilled if Lorentz covariance is dropped. These models illustrate a point made by Borchers in the proof of his two-dimensional CPT theorem for local nets: The Lorentz covariant net constructed from the wedge algebras of a given two-dimensional net may not be unique. It is also shown that in higher dimensions, the Lorentz boosts constructed by means of the modular groups of wedge algebras may act nonlocally in the directions parallel to the edge of the wedge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750147
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  • 10
    Electronic Resource
    Electronic Resource
    Generalized nuclearity conditions and the split property in quantum field theory (1991)
    Springer
    Letters in mathematical physics 23 (1991), S. 159-167 
    Details
    ISSN: 1573-0530
    Keywords: 81T05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Generalized nuclearity conditions that are applicable in arbitrary superselection sectors of a quantum field theory and to theories with a maximal temperature are discussed. They are shown to imply the (distal) split property and to impose specific restrictions on the spectral properties of modular operators associated with local algebras and vectors of compact energy support.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00703730
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