Dirac Equation on a Curved 2+1 Dimensional Hypersurface

Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact in mind, the following problem is studied in this work: when a spin 1/2 particle is constrained to move on a curved surface, is it possible to describe this particle without giving reference to the dimensions external to the surface? As a special case of this, a relativistic spin 1/2 particle which is constrained to move on a 2 + 1 dimensional hypersurface of the 3 + 1 dimensional Minkowskian spacetime is considered, and an effective Dirac equation for this particle is derived using the so-called thin layer method. Some of the results are compared with those obtained in a previous work by M. Burgess and B. Jensen.Comment: 5 pages. To be published in Modern Physics Letters

On the calculation of covariant expressions for Dirac bilinears

In this article, various approaches to calculate covariant expressions for the bilinears of Dirac spinors are presented. For this purpose, algebraic equations defining Dirac spinors are discussed. Following that, a covariant approach for spacetime parameterization is presented and the equations defining Dirac spinors are written fully in terms of Lorentz scalars. After presenting how the tensorial bilinears can be reduced to combinations of scalar bilinears with appropriate Lorentz structures, a covariant recipe for the calculation of scalar bilinears is provided.Comment: 10 pages, 1 figur

Regularized Weyl double copy

We propose a regularization procedure in the sourced Weyl double copy, a spinorial version of the classical double copy, such that it matches much more general results in the Kerr-Schild version. In the regularized Weyl double copy, the AdS and the Lifshitz black holes, which form the basis of the study of strongly coupled gauge theories at finite temperature through the AdS/CFT correspondence and its non-relativistic generalization, become treatable. We believe that this might pave the way for finding out a relation between the classical double copy and holograpy.Comment: Minor change

P-dalga ağır kuarkonyumların tvist-2 ışık konisi dağılım genlikleri ve psödoskaler ve vektör mezonlara çıftlenimleri.

The problem analyzed in this work is the calculation of the coupling of L = 1 axial-vector heavy quarkonia to vector and pseudo-scalar open flavor mesons. Calculations are based on light-cone QCD sum rules, with inputs from indepen- dently performed quark model calculations for the analysis of radially excited states. Those couplings are of interest for being inputs for effective theory calcu- lations on the quark content and transitions of axial-vector Xc/b mesons. Results involve profiles for the light-cone distribution amplitudes of charmonia and bot- tomonia, their respective leptonic decay constants and the mentioned coplings. Charmonium content of X(3872) is also discussed in light of the results. Ph.D. - Doctoral Progra

Eğri hiperyüzeylerde kuantum mekaniği.

In this work, Schrödinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit use of geometrical relations and the squeezing of a certain coordinate of space (or spacetime). The second is Dirac’s quantization procedure involving the modification of canonical quantization making use of the geometrical constraints. For the Dirac equation, only the first method will be considered. Lastly, the results of the two methods will be compared and some notes on the differences between the results will be included.M.S. - Master of Scienc