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
