Reconstruction in quantum field theory with a fundamental length

Journal Article · Wed Sep 15 04:00:00 EDT 2010 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3483691· OSTI ID:21483623

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)

In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex l-neighborhood of the real space and are localizable at scales large compared to l. The causality condition is formulated as continuity of the field commutator in an appropriate topology associated with the light cone. We prove that the relevant function spaces are nuclear and derive the kernel theorems for the corresponding classes of multilinear functionals, which provides the basis for the reconstruction procedure. Special attention is given to the accurate determination of the domain of the reconstructed quantum fields in the Hilbert space of states. We show that the primitive common invariant domain must be suitably extended to implement the (quasi)localizability and causality conditions.

• OSTI ID: 21483623
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 51; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AXIOMATIC FIELD THEORY
BANACH SPACE
CAUSALITY
COMMUTATORS
FIELD THEORIES
FUNCTIONALS
FUNCTIONS
HILBERT SPACE
KERNELS
LIGHT CONE
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SPACE
SPACE-TIME
TOPOLOGY
WIGHTMAN FIELD THEORY
YUKAWA NONLOCAL THEORY