Space-Time Noncommutativity, Discreteness of Time and Unitarity

Violation of unitarity for noncommutative field theory on compact space-times is considered. Although such theories are free of ultraviolet divergences, they still violate unitarity while in a usual field theory such a violation occurs when the theory is nonrenormalizable. The compactness of space-like coordinates implies discreteness of the time variable which leads to appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time. Violation of causality, among others, occurs also as the nonvanishing of the commutation relations between observables at space-like distances with a typical scale of noncommutativity. While this feature allows for a possible violation of the spin-statistics theorem, such a violation does not rescue the situation but makes the scale of causality violation as the inverse of the mass appearing in the considered model, i.e., even more severe. We also stress the role of smearing over the noncommutative coordinates entering the field operator symbols.Comment: 10 pages, plain LaTe

Searching for intrinsic charm in the proton at the LHC

Despite rather long-term theoretical and experimental studies, the hypothesis of the non-zero intrinsic (or valence-like) heavy quark component of the proton distribution functions has not yet been confirmed or rejected. The LHC with $pp$-collisions at $\sqrt{s}=$ 7--14 TeV will obviously supply extra unique information concerning the above-mentioned component of the proton. To use the LHC potential, first of all, one should select the parton-level (sub)processes (and final-state signatures) that are most sensitive to the intrinsic heavy quark contributions. To this end inclusive production of $c(b)$-jets accompanied by photons is considered. On the basis of the performed theoretical study it is demonstrated that the investigation of the intrinsic heavy quark contributions looks very promising at the LHC in processes such as $pp\rightarrow \gamma+ c(b)+X$.Comment: 13 pages, 6 figure

OGSA/Globus Evaluation for Data Intensive Applications

We present an architecture of Globus Toolkit 3 based testbed intended for evaluation of applicability of the Open Grid Service Architecture (OGSA) for Data Intensive Applications.Comment: To be published in the proceedings of the XIX International Symposium on Nuclear Electronics and Computing (NEC'2003), Bulgaria, Varna, 15-20 September, 200

Aharonov-Bohm Effect in Noncommutative Spaces

The Aharonov-Bohm effect on the noncommutative plane is considered. Developing the path integral formulation of quantum mechanics, we find the propagation amplitude for a particle in a noncommutative space. We show that the corresponding shift in the phase of the particle propagator due to the magnetic field of a thin solenoid receives certain gauge invariant corrections because of the noncommutativity. Evaluating the numerical value for this correction, an upper bound for the noncommutativity parameter is obtained.Comment: 2nd version, some clarifications added, the results compared with the existing experimental dat

Quantum Field Theory on the Noncommutative Plane with Eq(2)E_q(2) Symmetry

We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the $E_q(2)$-invariant measure on the noncommutative plane. With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane. Finally, we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the $E_q(2)$ quantum group.Comment: LaTeX, 26 page

Path Integrals with Generalized Grassmann Variables

We construct path integral representations for the evolution operator of q-oscillators with root of unity values of q-parameter using Bargmann-Fock representations with commuting and non-commuting variables, the differential calculi being q-deformed in both cases. For $q^2=-1$ we obtain a new form of Grassmann-like path integral.Comment: 9 pages, LaTe

Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates

We find that the momentum conjugate to the relative distance between two gravitating particles in their center of mass frame is a hyperbolic angle. This fact strongly suggests that momentum space should be taken to be a hyperboloid. We investigate the effect of quantization on this curved momentum space. The coordinates are represented by non commuting, Hermitian operators on this hyperboloid. We also find that there is a smallest distance between the two particles of one half times the Planck length.Comment: 18 pages Latex, 2 eps figure

Polynomial Algebras and Higher Spins

Polynomial relations for generators of $su(2)$ Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified Holstein-Primakoff transformations in finite dimensional Fock spaces. The connection between $su(2)$ Lie algebra and q-oscillators with a root of unity q-parameter is considered. The meaning of the polynomial relations from the point of view of quantum mechanics on a sphere are discussed.Comment: 8 pages, LaTe