The Fourier transform of confining potentials

The precise meaning of the Fourier transform of ‖x‖ν is examined. A general expression is given for real positive ν. For odd ν, derivatives of principal value integrals are obtained, while even ν gives rise to derivatives of the delta function.

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Bibliographische Detailangaben
Veröffentlicht in:	J. Math. Phys. (N.Y.); (United States) 1986-04, Vol.27 (4), p.936-937
Hauptverfasser:	Heiss, W. D., Welke, G. M.
Format:	Artikel
Sprache:	eng
Schlagworte:	645400 - High Energy Physics- Field Theory 658000 - Mathematical Physics- (-1987) CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ELEMENTARY PARTICLES Exact sciences and technology FIELD THEORIES FOURIER TRANSFORMATION Function theory, analysis GLUONS INTEGRAL TRANSFORMATIONS Mathematical methods in physics Physics PHYSICS OF ELEMENTARY PARTICLES AND FIELDS POSTULATED PARTICLES POTENTIALS QUANTUM CHROMODYNAMICS QUANTUM FIELD THEORY QUARKS TRANSFORMATIONS
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Beschreibung
Zusammenfassung:	The precise meaning of the Fourier transform of ‖x‖ν is examined. A general expression is given for real positive ν. For odd ν, derivatives of principal value integrals are obtained, while even ν gives rise to derivatives of the delta function.
ISSN:	0022-2488 1089-7658
DOI:	10.1063/1.527166