We present a deformed star-product for a particle in the presence of a magnetic monopole. The product is obtained within a self-dual quantization-dequantization scheme, with the correspondence between classical observables and operators defined with the help of a quaternionic Hilbert space, following work by Emch and Jadczyk. The resulting product is well defined for a large class of complex functions and reproduces (at first order in hbar) the Poisson structure of the particle in the monopole field. The product is associative only for quantized monopole charges, thus incorporating Dirac's quantization requirement.
Star-product in the presence of a monopole / J., Carinena; J., Gracia Bondia; Lizzi, Fedele; Marmo, Giuseppe; Vitale, Patrizia. - In: PHYSICS LETTERS A. - ISSN 0375-9601. - 374:35(2010), pp. 3614-3618. [10.1016/j.physleta.2010.06.069]
Star-product in the presence of a monopole
LIZZI, FEDELE;MARMO, GIUSEPPE;VITALE, PATRIZIA
2010
Abstract
We present a deformed star-product for a particle in the presence of a magnetic monopole. The product is obtained within a self-dual quantization-dequantization scheme, with the correspondence between classical observables and operators defined with the help of a quaternionic Hilbert space, following work by Emch and Jadczyk. The resulting product is well defined for a large class of complex functions and reproduces (at first order in hbar) the Poisson structure of the particle in the monopole field. The product is associative only for quantized monopole charges, thus incorporating Dirac's quantization requirement.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
