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This article is cited in 2 scientific papers (total in 2 papers)
Two classes of generalized functions used in nonlocal field theory
M. A. Soloviev P. N. Lebedev Physical Institute, Russian Academy of Sciences
Abstract:
We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space $S^0$ (which is the Fourier transform of the Schwartz space $\mathcal D$) and using test functions in the Gelfand–Shilov spaces $S^0_\alpha$. We prove that every functional defined on $S^0$ has the same carrier cones as its restrictions to the smaller spaces $S^0_\alpha$. As an application of this result, we derive a Paley–Wiener–Schwartz-type theorem for arbitrarily singular generalized functions of tempered growth and obtain the corresponding extension of Vladimirovs algebra of functions holomorphic in a tubular domain.
Keywords:
nonlocal quantum fields, causality, Wightman functions, analytic functionals, Hörmanders estimates, Paley–Wiener–Schwartz-type theorems.
Received: 02.07.2004
Citation:
M. A. Soloviev, “Two classes of generalized functions used in nonlocal field theory”, TMF, 143:2 (2005), 195–210; Theoret. and Math. Phys., 143:2 (2005), 651–663
Linking options:
https://www.mathnet.ru/eng/tmf1810https://doi.org/10.4213/tmf1810 https://www.mathnet.ru/eng/tmf/v143/i2/p195
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Abstract page: | 369 | Full-text PDF : | 220 | References: | 77 | First page: | 1 |
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