Dirac equation for quasi-particles in graphene and quantum field theory of their Coulomb interaction

There is evidence for existence of massless Dirac quasi-particles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. We revisit the derivation of Dirac equation in (1+2) dimensions obeyed by quasiparticles in graphene near the Dirac points. It is shown that parity operator in (1+2) dimensions play an interesting role and can be used for defining "conserved" currents resulting from the underlying Lagrangian for Dirac quasi-particles in graphene which is shown to have U_{A}(1)*U_{B}(1) symmetry. Further the quantum field theory (QFT) of Coulomb interaction of 2D graphene is developed and applied to vacuum polarization and electron self energy and the renormalization of the effective coupling g of this interaction and Fermi velocity $v_{f}$ which has important implications in the renormalization group analysis of g and v_{f}.Comment: 10 pages, some typos have been corrected, some references have been adde

Implementation and Effectiveness of International Environmental Regimes During the Process of Transformation in Russia

Hundreds or even thousands of international legal instruments on "the environment" are in existence. What happens to international environmental agreements once they are signed, and how does the process of implementing such agreements influence their effectiveness? These are the questions that motivate the IIASA project "Implementation and Effectiveness of International Environmental Commitments (IEC)". Research teams are examining these questions from many angles and with different methods. In this paper, the author examines the ways in which international environmental agreements are implemented in the former Soviet Union, especially Russia. The massive transformation under way in the former command economies poses interesting questions and many difficulties for scholars. Transformation affects behavior in all sectors of the society, and implementation of international environmental agreements is also intended to affect behavior. How can scholars disentangle the influences on behavior due to transformation and those due to implementation of international environmental agreements? Kotov examines the major elements of the transformation under way in Russia and focuses on how implementation of international environmental agreements might affect and be affected by the transformation. In doing so, he lays one foundation for disaggregating these different influences on behavior. Transformation is marked by the relative absence of planning and implementation because the old system of commands has collapsed and a new system has not yet effectively emerged. A major challenge for the new system is to manage the decentralization of authority and decision-making that accompanies the organization of society around markets rather than commands. Kotov notes that during the transformation process much more of the activity and policy planning that is relevant for implementation of international environmental agreements now takes place at the local level. Direct implementation of plans and standards has decreased markedly; the role of negotiation has increased, leading to widely varied outcomes. Under the command system, when the planning process was mobilized to implement an agreement, implementation was easier. Many decisions made during the transformation period will have long-term consequences for the implementation of international environmental agreements. Among these are choices about distribution and control over property rights. The IEC project is now sponsoring several in-depth case studies -- notably on the European acid rain agreement (including a study of implementing acid rain controls on the Kola Peninsula) and the agreements to control pollution in the Baltic Sea. Those empirical studies employ some of the concepts and questions elaborated in this paper