Abstract: We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion bialgebra. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can generate new solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As they depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory will be a noncommutative manifold. Similarly, gauge transformations should be allowed to depend on additional noncommutative parameters.
q-Quaternions and q-deformed su(2) instantons / Fiore, Gaetano. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 48:(2007), pp. 102301-102333.
q-Quaternions and q-deformed su(2) instantons
FIORE, GAETANO
2007
Abstract
Abstract: We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion bialgebra. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can generate new solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As they depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory will be a noncommutative manifold. Similarly, gauge transformations should be allowed to depend on additional noncommutative parameters.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.