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  • Articles  (2)
  • American Institute of Physics (AIP)  (2)
  • Mathematics  (2)
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  • Articles  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    Hyperfunction quantum field theory: Basic structural results (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2340-2359 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The choice of the class E' of generalized functions on space-time in which to formulate general relativistic quantum field theory (QFT) is discussed. A first step is to isolate a set of conditions on E' that allows a formulation of QFT in otherwise the same way as the original proposal by Wightman [Ark. Fys. 28, 129 (1965)], where E' is the class of tempered distributions. It is stressed that the formulation of QFT in which E' equals the class of Fourier hyperfunctions on space-time meets the following requirements: (A) Fourier hyperfunctions generalize tempered distributions thus allowing more singular fields as suggested by concrete models; (B) Fourier hyperfunction quantum fields are localizable both in space-time and in energy-momentum space thus allowing the physically indispensable standard interpretation of Poincaré covariance, local commutativity, and localization of energy-momentum spectrum; and (C) in Fourier hyperfunction quantum field theory almost all the basic structural results of "standard'' QFT (existence of a PCT operator, spin-statistics theorems, existence of a scattering operator, etc.) hold. Finally, a short introduction to that part of Fourier hyperfunction theory needed in this context is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528564
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  • 2
    Electronic Resource
    Electronic Resource
    Closure of field operators, asymptotic Abelianness, and vacuum structure in hyperfunction quantum field theory (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5098-5111 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Though, in contrast to standard quantum field theory (QFT), the tensor-algebra over the test-function space of hyperfunction quantum field theory has no local structure, the localization properties of states on this algebra can be used to derive asymptotic Abelianness in spacelike directions. Again, in contrast to standard QFT, the closure of (Hermitian) field operators can destroy localization properties. This problem is addressed in a natural modification of the definition of the closure, called the local closure. This allows one, in conjunction with asymptotic Abelianness, to define a proper reduction of the field algebra to the subspace of the translation invariant states, and to investigate the dimension of this subspace. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532560
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