Leading twist light cone distribution amplitudes (LCDAs) are key ingredients in calculating various hadronic amplitudes using light cone QCD sum rules. This work concentrates on calculating the leading twist LCDAs of P-wave heavy quarkonia. Quark model wavefunctions for the ground, first and second excited states of P-wave charmonia and bottomonia have been calculated, and are used for calculating the relevant LCDAs and leptonic decay constants.

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Interest on (2+1)-dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behavior 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 Burgess and Jensen.

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.

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