A note on the path integral representation for Majorana fermions

Majorana fermions are currently of huge interest in the context of nanoscience and condensed matter physics. Different to usual fermions, Majorana fermions have the property that the particle is its own anti-particle thus, they must be described by real fields. Mathematically, this property makes nontrivial the quantization of the problem due, for instance, to the absence of a Wick-like theorem. In view of the present interest on the subject, it is important to develop different theoretical approaches in order to study problems where Majorana fermions are involved. In this note we show that Majorana fermions can be studied in the context of field theories for constrained systems. Using the Faddeev-Jackiw formalism for quantum field theories with constraints, we derived the path integral representation for Majorana fermions. In order to show the validity of the path integral we apply it to an exactly solvable problem. This application also shows that it is rather simple to perform systematic calculations on the basis of the present framework.Comment: 7 pages, to be published in Journal of Physics A: Mathematical and Theoretica

Phase-Space Coalescence for heavy and light quarks at RHIC

We review the application and successes of a phase-space coalescence plus fragmentation model that has been applied for hadronization at RHIC. The physical concept is discussed together with the practical implementation. The robustness of main predictions is reviewed together with several open issues like relevance of three dimensional calculation, finite width of the wave functions, effects of quark masses, energy-entropy conservation, space-momentum correlation. Eventually the relevance of coalescence also for the study of the microscopic interaction of heavy quarks is highlighted.Comment: Talk given at the Zimanyi 75 Memorial Workshop on "Hadronic and Quark Matter", Budapest, July 2-4, 2007. To appear in The European Physical Journal (Special Topics

Evidence for two competing order parameters in underdoped cuprates superconductors from a model analysis of the Fermi-arc effects

Preformed pairs above $T_c$ and the two-gap scenarios are two main proposals for describing the low doping pseudogap phase of high-$T_c$ cuprates. Very recent angle-resolved photoemission experiments have shown features which were interpreted as evidence for preformed pairs. Here it is shown that those results can be explained also in the context of the two-gap scenario if self-energy effects are considered. The discussion is based on the $d$-CDW theory or the flux phase of the $t-J$ model.Comment: 4 pages, 4 figures, accepted for publication in Phys. Rev. Let

The reality of rights. On horizontal and vertical relationships in law

A pesar de las novedades de las últimas décadas, el pensamiento jurídico todavía parece preso en la creencia positivista que sólo lo que es fortalecido por la sanción jurídica del Estado puede tener valor jurídico. Algunas reticencias acerca del soft law son una manifestación de esta actitud, que disminuye la importancia de las obligaciones primarias, y que proviene del hecho de que no se toman en serio las consecuencias normativas de las relaciones sociales, olvidando la importancia que las obligaciones horizontales tienen para el orden social y jurídico. De esta manera, no se puede comprender la realidad de los derechos, cuya eficacia está garantizada principalmente por el reconocimiento mutuo entre los sujetos de las relaciones.Despite many developments in recent decades, legal theory still seems prisoner to the positivist belief that only norms backed by state sanction can be deemed legal. The misgivings voiced concerning the notion of ‘soft law’ are evidence of this belief. This stance, which minimizes the significance of primary obligations, stems from the failure to take seriously the normative capacity of social relations, and thereby overlooks the foundational value that horizontal obligations have for the social and legal order. And in doing so, it risks misunderstanding the reality of rights, whose efficacy is guaranteed first and foremost through the mutual recognition between subjects in a relationship