Quantum field theory with a fundamental length: A general mathematical framework

Journal Article · Tue Dec 15 04:00:00 EST 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3269595· OSTI ID:21294529

Soloviev, M A ^[1]

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1. I. E. Tamm Department of Theoretical Physics, P. N. Lebedev Physical Institute, Leninsky Prospect 53, Moscow 119991 (Russian Federation)

We review and develop a mathematical framework for nonlocal quantum field theory (QFT) with a fundamental length. As an instructive example, we re-examine 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 the Wightman-type axioms with an exponential high-energy bound, which does not depend on n, contrary to the claims in 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 by Bruening and Nagamachi [J. Math. Phys. 45, 2199 (2004)] in terms of ultrahyperfunctions, the presented theory obviously becomes local as l tends to zero.

• OSTI ID: 21294529
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 50; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
CAUSALITY
GAUSS FUNCTION
LIGHT CONE
LORENTZ INVARIANCE
WIGHTMAN FIELD THEORY
YUKAWA NONLOCAL THEORY