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Article overview
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Reconstruction in quantum field theory with a fundamental length | Michael A. Soloviev
; | Date: |
16 Dec 2010 | Abstract: | 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. | Source: | arXiv, 1012.3546 | Services: | Forum | Review | PDF | Favorites |
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