Kappa-deformed oscillators, the choice of star product and free kappa-deformed quantum fields

In order to obtain free kappa-deformed quantum fields (with c-number commutators) we proposed new concept of kappa-deformed oscillator algebra [1] and the modification of kappa-star product [2], implementing in the product of two quantum fields the change of standard kappa-deformed mass-shell conditions. We recall here that the kappa-deformed oscillators recently introduced in [3]-[5] lie on standard kappa-deformed mass-shell. Firstly, we study kappa-deformed fields with the standard kappa-star product, what implies that in the oscillator algebra the corresponding kappa-deformed oscillators lie on standard kappa-deformed mass-shell. We argue that for the kappa-deformed algebra of such field oscillators which carry fourmomenta on kappa-deformed mass-shell it is not possible to obtain the free quantum kappa-deformed fields with the c-number commutators. Further, we study kappa-deformed quantum fields with the modified kappa-star product which implies the modification of kappa-deformed mass-shell. We obtain large class of kappa-deformed statistics depending on six arbitrary functions which provides the c-number field commutator functions. Such general class of kappa-oscillators can be described as the kappa-deformation of standard oscillator algebra obtained by composing general kappa-deformed multiplication with the deformation of the flip operator.Comment: 21 pages;v3 more clearly exposed aims and results in the paper; the version which will appear in Journ.Phys.

MODIFICATION OF THE CENTRAL REGION IN THE RIKEN AVF CYCLOTRON FOR ACCELERATION AT THE H=1 RF HARMONIC

Abstract A highly advanced upgrade plan of the RIKEN AVF cyclotron is under way. The study is focused on the formulation of the new acceleration regimes in the AVF cyclotron by detailed orbit simulations. The extension of the acceleration energy region of light ions towards higher energies in the existing RF harmonic equal to 2 and the modification of the central geometry for the RF harmonic equal to 1 to allow an acceleration of protons at several tens of MeV are considered. The substantial redesign of the central electrode structure is needed to accelerate protons with reasonable values of the dee voltage. The new inflector geometry and the optimized central electrode structure have been formulated for the upgrade