Quantum space and quantum completeness

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.Comment: 13 pages, minor revision, published in JHE

The Shape and Profile of the Milky Way Halo as Seen by the Canada-France-Hawaii Telescope Legacy Survey

We use Canada-France-Hawaii Telescope Legacy Survey data for 170 deg^2, recalibrated and transformed to the Sloan Digital Sky Survey ugri photometric system, to study the distribution of near-turnoff main-sequence stars in the Galactic halo along four lines of sight to heliocentric distances of ~35 kpc. We find that the halo stellar number density profile becomes steeper at Galactocentric distances greater than R_(gal) ~ 28 kpc, with the power-law index changing from n_(inner) = –2.62 ± 0.04 to n_(outer) = –3.8 ± 0.1. In particular, we test a series of single power-law models and find them to be strongly disfavored by the data. The parameters for the best-fit Einasto profile are n = 2.2 ± 0.2 and R_e = 22.2 ± 0.4 kpc. We measure the oblateness of the halo to be q ≡ c/a = 0.70 ± 0.01 and detect no evidence of it changing across the range of probed distances. The Sagittarius stream is detected in the l = 173° and b = –62° direction as an overdensity of [Fe/H] ~ -1.5 dex stars at R_(gal) ~ 32 kpc, providing a new constraint for the Sagittarius stream and dark matter halo models. We also detect the Monoceros stream as an overdensity of [Fe/H] > -1.5 dex stars in the l = 232° and b = 26° direction at R_(gal) ≲ 25 kpc. In the two sight lines where we do not detect significant substructure, the median metallicity is found to be independent of distance within systematic uncertainties ([Fe/H] ~ -1.5 ± 0.1 dex)

Differential forms and k-Minkowski spacetime from extended twist

We analyze bicovariant differential calculus on $\kappa$-Minkowski spacetime. It is shown that corresponding Lorentz generators and noncommutative coordinates compatible with bicovariant calculus cannot be realized in terms of commutative coordinates and momenta. Furthermore, $\kappa$-Minkowski space and NC forms are constructed by twist related to a bicrossproduct basis. It is pointed out that the consistency condition is not satisfied. We present the construction of $\kappa$-deformed coordinates and forms (super-Heisenberg algebra) using extended twist. It is compatible with bicovariant differential calculus with $\kappa$-deformed $\mathfrak{igl}(4)$-Hopf algebra. The extended twist leading to $\kappa$-Poincar\'{e}-Hopf algebra is also discussed.Comment: 15 pages, minor typos corrected to match the published versio

Učinak antiepileptika na kognitivne evocirane potencijale P300 u bolesnika s epilepsijom

Epilepsy is one of the most prevalent chronic neurological diseases, affecting about 70 million people worldwide. Patients with epilepsy often encounter cognitive dysfunction, which is influenced by different factors including age at the onset of epilepsy, etiology of epilepsy, type of seizures, seizure frequency and duration, psychiatric comorbidity, and antiepileptic drug (AED) therapy. Event-related potentials are useful, noninvasive, objective clinical and research instrument for evaluation of cognitive functions in patients. The aim of this study was to investigate and determine the effect of AED monotherapy and polytherapy on cognitive changes in patients with epilepsy, detected with P300 event-related potentials and compared with age- and gender-matched healthy individuals. The study was conducted in 82 patients with generalized and focal epilepsy and 82 healthy individuals aged 18-65 years. Cognitive evoked P300 potentials were recorded in all study subjects using auditory ‘oddball’ paradigm. The results showed the patients taking AED polytherapy to have a significantly longer P300 latency and significantly lower N200-P300 amplitude. These results indicate that AED polytherapy might worsen cognitive impairment in patients with epilepsy.Epilepsija je jedna od najčešćih kroničnih neuroloških bolesti od koje boluje oko 70 milijuna ljudi diljem svijeta. Bolesnici s epilepsijom često imaju poremećaj kognitivnih funkcija uzrokovan početkom bolesti, vrstom epileptičkih napadaja, trajanjem bolesti i antiepileptičkim lijekovima. Kognitivni evocirani potencijali P300 su korisna, neinvazivna, objektivna klinička i istraživačka metoda za ispitivanje kognitivnih funkcija. Cilj ovoga istraživanja bio je ispitati i utvrditi učinak antiepileptičkih lijekova (AEL) u monoterapiji i politerapiji na kognitivne promjene u bolesnika s epilepsijom uz pomoć kognitivnih evociranih potencijala P300 i usporediti ih sa zdravim pojedincima usklađenim prema dobi i spolu. U ispitivanju je sudjelovalo 82 bolesnika s generaliziranom i žarišnom epilepsijom i 82 zdrava pojedinca u dobi od 18-65 godina. Kognitivni evocirani potencijali P300 su snimani koristeći slušnu oddball paradigmu. Rezultati ove studije ukazuju na to da bolesnici na politerapiji AEL imaju značajno produženu latenciju vala P300 i značajno nižu amplitudu N200-P300. Prema rezultatima ove studije može se zaključiti kako politerapija AEL u bolesnika s epilepsijom može dovesti do pogoršanja kognitivnog poremećaja

Vacuum energy and the cosmological constant problem in κ\kappa-Poincar\'e invariant field theories

We investigate the vacuum energy in $\kappa$-Poincar\'e invariant field theories. It is shown that for the equivariant Dirac operator one obtains an improvement in UV behavior of the vacuum energy and therefore the cosmological constant problem has to be revised.Comment: improved version, 15 page

Involutive representations of coordinate algebras and quantum spaces

We show that $\frak{su}(2)$ Lie algebras of coordinate operators related to quantum spaces with $\frak{su}(2)$ noncommutativity can be conveniently represented by $SO(3)$-covariant poly-differential involutive representations. We show that the quantized plane waves obtained from the quantization map action on the usual exponential functions are determined by polar decomposition of operators combined with constraint stemming from the Wigner theorem for $SU(2)$. Selecting a subfamily of $^*$-representations, we show that the resulting star-product is equivalent to the Kontsevich product for the Poisson manifold dual to the finite dimensional Lie algebra $\mathfrak{su}(2)$. We discuss the results, indicating a way to extend the construction to any semi-simple non simply connected Lie group and present noncommutative scalar field theories which are free from perturbative UV/IR mixing.Comment: 29 pages, several paragraphs added, published in JHE