The Evolution Function of the Operator − (−Δ)v

The Evolution Function of the Operator − (−Δ)v

The evolution function of the differential operator −(−Δ) v in a d -dimensional Euclidean space is calculated. We obtain its analytic expression through the Fox-Wright psi-functions, which is well-defined for both integer and noninteger values of v and d . Possible applications of the obtained funct...

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Veröffentlicht in:Moscow University physics bulletin 2019, Vol.74 (1), p.17-23
Hauptverfasser: Wachowski, W. N., Pronin, P. I.
Format: Artikel
Sprache:eng
Schlagworte:
Differential equations
Euclidean geometry
Euclidean space
Evolution
Field theory
Fractional calculus
Mathematical analysis
Mathematical and Computational Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum field theory
Quantum theory
Theoretical
Theoretical and Mathematical Physics
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Zusammenfassung:The evolution function of the differential operator −(−Δ) v in a d -dimensional Euclidean space is calculated. We obtain its analytic expression through the Fox-Wright psi-functions, which is well-defined for both integer and noninteger values of v and d . Possible applications of the obtained functions in quantum field theory and the connection with fractional calculus are discussed.
ISSN:0027-1349
1934-8460
DOI:10.3103/S0027134919010168