Effective Interactions of Planar Fermions in a Strong Magnetic Field-the Effect of Landau Level Mixing

We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is sytematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-fermi interactions. The importance of Landau level mixing for long-range interactions is especially emphasized. We also calculate the edge-current for a finite sample.Comment: 15 pages, plain te

Canonical Commutation Relations in The Schwinger Model

We give the first operator solution of the Schwinger model that obeys the canonical commutation relations in a covariant guage.Comment: 7 page

Genome-wide fine-scale recombination rate variation in Drosophila melanogaster

Estimating fine-scale recombination maps of Drosophila from population genomic data is a challenging problem, in particular because of the high background recombination rate. In this paper, a new computational method is developed to address this challenge. Through an extensive simulation study, it is demonstrated that the method allows more accurate inference, and exhibits greater robustness to the effects of natural selection and noise, compared to a well-used previous method developed for studying fine-scale recombination rate variation in the human genome. As an application, a genome-wide analysis of genetic variation data is performed for two Drosophila melanogaster populations, one from North America (Raleigh, USA) and the other from Africa (Gikongoro, Rwanda). It is shown that fine-scale recombination rate variation is widespread throughout the D. melanogaster genome, across all chromosomes and in both populations. At the fine-scale, a conservative, systematic search for evidence of recombination hotspots suggests the existence of a handful of putative hotspots each with at least a tenfold increase in intensity over the background rate. A wavelet analysis is carried out to compare the estimated recombination maps in the two populations and to quantify the extent to which recombination rates are conserved. In general, similarity is observed at very broad scales, but substantial differences are seen at fine scales. The average recombination rate of the X chromosome appears to be higher than that of the autosomes in both populations, and this pattern is much more pronounced in the African population than the North American population. The correlation between various genomic features—including recombination rates, diversity, divergence, GC content, gene content, and sequence quality—is examined using the wavelet analysis, and it is shown that the most notable difference between D. melanogaster and humans is in the correlation between recombination and diversity

Sperm DNA fragmentation: A new guideline for clinicians

Sperm DNA integrity is crucial for fertilization and development of healthy offspring. The spermatozoon undergoes extensive molecular remodeling of its nucleus during later phases of spermatogenesis, which imparts compaction and protects the genetic content. Testicular (defective maturation and abortive apoptosis) and post-testicular (oxidative stress) mechanisms are implicated in the etiology of sperm DNA fragmentation (SDF), which affects both natural and assisted reproduction. Several clinical and environmental factors are known to negatively impact sperm DNA integrity. An increasing number of reports emphasizes the direct relationship between sperm DNA damage and male infertility. Currently, several assays are available to assess sperm DNA damage, however, routine assessment of SDF in clinical practice is not recommended by professional organizations

On bound states and non-trivial fixed points in quantum field theories

The calculation of the binding energies in Quantum Field Theories (QFT's) is a hard and long standing problem. Even for weakly coupled field theories like QED the extraction of information on bound states from the perturbative expansion is considered an "art". In the first part of this thesis we define those bound states that can be recovered from the perturbative expansion (threshold bound states) and calculate their mass in various models. It is shown that the method of Pade approximation and the Bethe-Salpeter equation (supplemented by a proof of absence of on mass shell singularities) provide a systematic way of calculating threshold bound states masses from the perturbative expansion of the S-matrix. We check these methods on 1+1 and 2+1 dimensional models where there exist a good expansion for the S-Matrix i.e. either weak coupling or 1/N. In the second part of this thesis a less rigorous approach is taken. This part concentrates on the B=2 sector of the SU (3) Skyrme model. We show that one can generate classical configurations (skyrmions) corresponding to bound states of two particles of an effective field theory (the Skyrme model), starting from classical solutions of the euclidean SU(3) Yang-Mills theory. The parity doubling of the ground state in this sector is also investigated. The third and last part deals with non trivial fixed points in QFT's. It is shown that the infra-red fixed point of the chiral phase transition in d=3 is the critical Gross- Neveu model. This is yet another proof to the nonperturbative renormalizability of four- Fermi interactions in 2+1 dimensions. The critical exponents of this phase transition are calculated within the 1/N expansion. The renormalizability of the GN model is also demonstrated explicitly to next to leading order in l/N by calculating β function, effective potential and ultraviolet dimension of various operators. [more abstract]Science, Faculty ofPhysics and Astronomy, Department ofGraduat