Djordje Sijacki#
Short laudatio by A.W. Wolfendale#
Djordje Sijacki made a significant contribution at the international level in the fields of symmetry groups representation theory and the symmetry based approach to particle physics and gravity theories.
Sijacki is the world leading expert in the subject of the quantum mechanical representations of the SL(n,R) groups. There was a long standing problem in physics and mathematics literature about existence and the form of their spinorial representations. Sijacki succeeded to find the complete solution of the (infinitely many) infinite-dimensional unitary irreducible representations of SL(3,R) and SL(4,R), which was acknowledged by leading mathematicians as well. Recently, he achieved to generalize the Gell-Mann Lie algebra decontraction formula and extended the explicite closed-form solution of the non-compact matrix elements for all infinite-dimensional representations to the general SL(n,R) case, thus making an important breakthrough in a few decades old subject.
Sijacki generalized the algebraic approach to hadron resonances spectroscopy of Dothan, Gell-Mann and Ne'eman to the relativistic case and developed the Affine Symmetry model that fits notably with the experimentally observed Regge trajectories of hadronic resonances. Furthermore, with Yuval Ne'eman, he proposed the "Chromogravity" theory, an effective description of the QCD theory in the Infra-Red region based on the colorless di-gluon configurations. He showed that the IR sector of the QCD gauge can be described by a pseudo Generalized Coordinate Transformations, and thus he developed a pseudo-gravity formulation of the confining QCD sector. His research on Chromogravity yields a QCD based dynamical explanation of the Regge trajectories of hadrons and provides their previously known famous linear spin vs. mass-squared relation.
Sijacki played an important role in development of the Metric-Affine, i.e. Gauge-Affine, generalization of Einstein's General Relativity theory in the quantum region. He succeeded to construct a realistic model, with a spontaneous symmetry breaking scenario, that reduces to the Poincare gauge theory of gravity. He showed that the Einstein's world tensor notion can be extended to the generic curved space "world spinors" as well by making use of the infinite-component GL(4,R) spinorial matter fields (there are no such finite fields).
He achieved an explicite construction of the world spinor fields, and managed recently to amplify the result by generalizing the famous Dirac equation to an infinite-component equation in a generic curved space. In particular, he provided an explicite solution in the 3D case, thus provided for the first time a Dirac-like equation for the General Coordinate Transformations spinors. Moreover, Sijacki extended the gravity world spinor constructions to the case of the spinning p-branes objects in a generic curved space.
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