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Quantum field theory with a fundamental length. A general mathematical framework | | Michael A. Soloviev
; | | Date: |
3 Dec 2009 | | Abstract: | We review and develop a mathematical framework for nonlocal quantum field
theory with a fundamental length. As an instructive example, we reexamine the
normal ordered Gaussian function of a free field and find the primitive
analyticity domain of its n-point vacuum expectation values. This domain is
smaller than the usual future tube of local QFT, but we prove that in
difference variables, it has the same structure of a tube whose base is the
(n-1)-fold product of a Lorentz invariant region. It follows that this model
satisfies Wightman-type axioms with an exponential high-energy bound which does
not depend on n, contrary to the claims in the literature. In our setting, the
Wightman generalized functions are defined on test functions analytic in the
complex l-neighborhood of the real space, where l is an n-independent constant
playing the role of a fundamental length, and the causality condition is
formulated with the use of an analogous function space associated with the
light cone. In contrast to the scheme proposed in Ref. [11] in terms of
ultra-hyperfunctions, the presented theory obviously becomes local as l tends
to zero. | | Source: | arXiv, 0912.0595 | | Services: | Forum | Review | PDF | Favorites | |
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