Dirac, Majorana, Weyl in 4d

This is a review of some elementary properties of Dirac, Weyl and Majorana spinors in 4d. We focus in particular on the differences between massless Dirac and Majorana fermions, on one side, and Weyl fermions, on the other. We review in detail the definition of their effective actions, when coupled to (vector and axial) gauge fields, and revisit the corresponding anomalies using the Feynman diagram method with different regularizations. Among various well known results we stress in particular the regularization independence in perturbative approaches, while not all the regularizations fit the non-perturbative ones. As for anomalies, we highlight in particular one perhaps not so well known feature: the rigid relation between chiral and trace anomalies.Comment: 38 pages, 3 figures, section 5, Appendix A and Appendix C new, several typos correcte

Evolution of universes in causal set cosmology

The causal set approach to the problem of quantum gravity is based on the hypothesis that spacetime is fundamentally discrete. Spacetime discreteness opens the door to novel types of dynamical law for cosmology and the Classical Sequential Growth (CSG) models of Rideout and Sorkin form an interesting class of such laws. It has been shown that a renormalisation of the dynamical parameters of a CSG model occurs whenever the universe undergoes a Big Crunch–Big Bang bounce. In this paper we propose a way to model the creation of a new universe after the singularity of a black hole. We show that renormalisation of dynamical parameters occurs in a CSG model after such a creation event. We speculate that this could realise aspects of Smolin's Cosmological Natural Selection proposal

Noninvasive Assessment of Antenatal Hydronephrosis in Mice Reveals a Critical Role for Robo2 in Maintaining Anti-Reflux Mechanism

Antenatal hydronephrosis and vesicoureteral reflux (VUR) are common renal tract birth defects. We recently showed that disruption of the Robo2 gene is associated with VUR in humans and antenatal hydronephrosis in knockout mice. However, the natural history, causal relationship and developmental origins of these clinical conditions remain largely unclear. Although the hydronephrosis phenotype in Robo2 knockout mice has been attributed to the coexistence of ureteral reflux and obstruction in the same mice, this hypothesis has not been tested experimentally. Here we used noninvasive high-resolution micro-ultrasonography and pathological analysis to follow the progression of antenatal hydronephrosis in individual Robo2-deficient mice from embryo to adulthood. We found that hydronephrosis progressed continuously after birth with no spontaneous resolution. With the use of a microbubble ultrasound contrast agent and ultrasound-guided percutaneous aspiration, we demonstrated that antenatal hydronephrosis in Robo2-deficient mice is caused by high-grade VUR resulting from a dilated and incompetent ureterovesical junction rather than ureteral obstruction. We further documented Robo2 expression around the developing ureterovesical junction and identified early dilatation of ureteral orifice structures as a potential fetal origin of antenatal hydronephrosis and VUR. Our results thus demonstrate that Robo2 is crucial for the formation of a normal ureteral orifice and for the maintenance of an effective anti-reflux mechanism. This study also establishes a reproducible genetic mouse model of progressive antenatal hydronephrosis and primary high-grade VUR

A manifestly covariant framework for causal set dynamics

We propose a manifestly covariant framework for causal set dynamics. The framework is based on a structure, dubbed covtree, which is a partial order on certain sets of finite, unlabeled causal sets. We show that every infinite path in covtree corresponds to at least one infinite, unlabeled causal set. We show that transition probabilities for a classical random walk on covtree induce a classical measure on the -algebra generated by the stem sets

If time had no beginning: growth dynamics for past-infinite causal sets

We explore whether the growth dynamics paradigm of causal set theory is compatible with past-infinite causal sets. We modify the classical sequential growth dynamics of Rideout and Sorkin to accommodate growth 'into the past' and discuss what form physical constraints such as causality could take in this new framework. We propose convex-suborders as the 'observables' or 'physical properties' in a theory in which causal sets can be past-infinite and use this proposal to construct a manifestly covariant framework for dynamical models of growth for past-infinite causal sets