Andjelo Samsarov

κ-Minkowski spacetime and the star product realizations

We investigate a Lie algebra-type κ-deformed Minkowski spacetime with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of κ-Minkowski space. The coproduct and the star product corresponding to each of them are found. An explicit connection between realizations and orderings is established and the relation between the coproduct and the star product, provided through an exponential map, is proved. Utilizing the properties of the natural realization, we construct a scalar field theory on κ-deformed Minkowski space and show that it is equivalent to the scalar, nonlocal, relativistically invariant field theory on the ordinary Minkowski space. This result is universal and does not depend on the realizations, i.e. the orderings, used.

SCALAR FIELD THEORY ON κ-MINKOWSKI SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE

We investigate the properties of κ-Minkowski space–time by using representations of the corresponding deformed algebra in terms of undeformed Heisenberg–Weyl algebra. The deformed algebra consists of κ-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 advantage 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 for κ-Minkowski space–time. 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 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 tachyonic modes and basically of the very same form. The issue of Lorentz invariance of the theory is also discussed.

Electron capture and scaling anomaly in polar molecules

Abstract We present a new analysis of the electron capture mechanism in polar molecules, based on von Neumanns theory of self-adjoint extensions. Our analysis suggests that it is theoretically possible for polar molecules to form bound states with electrons, even with dipole moments smaller than the critical value D 0 = 1.63 × 10 −18 esu cm . We argue that the quantum mechanical scaling anomaly is responsible for the formation of these bound states.

Quantum statistics and noncommutative black holes

We study the behavior of a scalar field coupled to a noncommutative black hole which is described by a

κ-deformation of phase space; generalized Poincaré algebras and R-matrix

\ensuremath{\kappa}

Effects of Noncommutativity on the Black Hole Entropy

-cylinder Hopf algebra. We introduce a new class of realizations of this algebra which has a smooth limit as the deformation parameter vanishes. The twisted flip operator is independent of the choice of realization within this class. We demonstrate that the

Different realizations ofκ-momentum space

R

Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole

-matrix is quasi-triangular up to the first order in the deformation parameter. Our results indicate how a scalar field might behave in the vicinity of a black hole at the Planck scale.

Light-like κ-deformations and scalar field theory via Drinfeld twist

A bstractWe deform a phase space (Heisenberg algebra and corresponding coalgebra) by twist. We present undeformed and deformed tensor identities that are crucial in our construction. Coalgebras for the generalized Poincaré algebras have been constructed. The exact universal R-matrix for the deformed Heisenberg (co)algebra is found. We show, up to the third order in the deformation parameter, that in the case of κ-Poincaré Hopf algebra this R-matrix can be expressed in terms of Poincaré generators only. This implies that the states of any number of identical particles can be defined in a κ-covariant way.

Noncommutative duality and fermionic quasinormal modes of the BTZ black hole

The BTZ black hole geometry is probed with a noncommutative scalar field which obeys the κ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton’s constant due to the effects of the noncommutativity.