Zoran Skoda meljAbs

Klju?ne rije?i: renormalization, Coulomb gauge

The structure of linear energy divergences is analyzed on the example of one graph to three-loop order. Such dangerous divergences do cancel when all graphs are added, but next-to-leading divergences do not cancel out.

Autori: Andra?i, An?elka; Taylor, J. C. Naslov: Renormalization in Coulomb gauge QCD Izvornik: Annals of physics (0003-4916) 326 (2011), 4; 1053-1069

Klju?ne rije?i: renormalization, qcd, coulomb gauge

In the Coulomb gauge of QCD, the Hamiltonian contains a nonlinear Christ-Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ-Lee term. We find that they cannot.

Autori: Kova?evi?, Domagoj Naslov: Real forms of dual pairs g2xh in g of type E6, E7 and E8 Izvornik: Journal of lie theory (0949-5932) 21 (2011), 2; 417-426

Klju?ne rije?i: dual pair, dual form

Let g be a complex Lie algebra of type En and let gxh be a dual pair in g. In this paper, we look for possible real forms of gxh. It turns out that for each n and for all real forms, say aoxho$ of gxh, there exists a real form go of g such that aoxho embedds into go.

Autori: Meljanac, Stjepan; Kre?i∞-Juri?; Sa?a Naslov: Differential structure on kappa-Minkowski space and kappa-Poincaré algebra Izvornik: International journal of modern physics A (0217-751X) 26 (2011), 10; 3385-3402

Klju?ne rije?i: kappa-Minkowski space, realizations, Lorenz algebra, differential forms

We construct realizations of the generators of the ∞-Minkowski space and ∞-Poincaré algebra as formal power series in the h-adic extension of the Weyl algebra. The Hopf algebra structure of the ∞-Poincaré algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on ∞-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the ∞-Minkowski space.

Autori: Meljanac, Stjepan; Meljanac, Daniel; Samsarov, Andjelo; Stojic, Marko Naslov: Kappa Snyder deformations of Minkowski spacetime, realizations, and Hopf algebra Izvornik: Physical Review D - Particles, Fields, Gravitation, and Cosmology (1550-7998) 83 (2011); 065009-1-065009-16

Klju?ne rije?i: kappa-deformed space, Snyder space, Hopf algebra

We present Lie-algebraic deformations of Minkowski space with undeformed Poincaré algebra. These deformations interpolate between Snyder and kappa-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. By introducing modules, it is shown that although deformed and undeformed structures are not isomorphic at the level of vector spaces, they are however isomorphic at the level of Hopf algebraic action on corresponding modules. Invariants and tensors with respect to Lorentz algebra are discussed. A general mapping from kappa-deformed Snyder to Snyder space is constructed. Deformed Leibniz rule, the Hopf structure and star product are found. Special cases, particularly Snyder and kappa-Minkowski in Maggiore-type realizations are discussed. The same generalized Hopf algebraic structures are as well considered in the case of an arbitrary allowable kind of realisation and results are given perturbatively up to second order in deformation parameters.

Meljanac, Stjepan; Samsarov, Andjelo. Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance. // International journal of modern physics A. 26 (2011) , 7 & 8; 1439-1468

We investigate the properties of kappa-Minkowski spacetime by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg-Weyl algebra. The deformed algebra consists of kappa-Poincare algebra extended with the generators of the deformed Weyl algebra. The part of deformed algebra, generated by rotation, boost and momentum generators, is described by the Hopf algebra structure. The approach used in our considerations is completely Lorentz covariant. We further use an adventages of this approach to consistently construct a star product which has a property that under integration sign it can be replaced by a standard pointwise multiplication, a property that was since known to hold for Moyal, but not also for kappa-Minkowski spacetime. This star product also has generalized trace and cyclic properties and the construction alone is accomplished by considering a classical Dirac operator representation of deformed algebra and by requiring it to be hermitian. We find that the obtained star product is not translationally invariant, leading to a conclusion that the classical Dirac operator representation is the one where translation invariance cannot simultaneously be implemented along with hermiticity. However, due to the integral property satisfied by the star product, noncommutative free scalar field theory does not have a problem with translation symmetry breaking and can be shown to reduce to an ordinary free scalar field theory without nonlocal features and tachionic modes and basicaly of the very same form. The issue of Lorentz invariance of the theory is also discussed.

?koda, Zoran. Heisenberg double versus deformed derivatives. // International journal of modern physics A. 26 (2011) , 27 & 28; 4845-4854

Bardek, Velimir; Feinberg Joshua; Meljanac, Stjepan. Fluctuations around Periodic BPS-Density Waves in the Calogero Model. // The Journal of high energy physics. 08 (2010) ; 018-051