Chiral Parametrization of QCD Vector Field in SU(3)

The chiral parametrization of gluons in SU(3) QCD is proposed extending an approach developed earlier for SU(2) case. A color chiral field is introduced, gluons are chirally rotated, and vector component of rotated gluons is defined on condition that no new color variables appeared with the chiral field. This condition associates such a vector component with SU(3)/U(2) coset plus an U(2) field. The topological action in SU(3) QCD is derived. It is expressed in terms of axial vector component of rotated gluons. The vector field in CP^2 sector is studied in new variables of chiral parametrization.Comment: 17 page

Color Bosonization, Chiral Parametrization of Gluonic Field and QCD Effective Action

We develop a color bosonization approach to treatment of QCD gauge field (''gluons'') at low energies in order to derive an effective color action of QCD taking into account the quark chiral anomaly in the case of SU(2) color.. We have found that there exists such a region in the chiral sector of color space, where a gauge field coincides with of chirally rotated vector field, while an induced axial vector field disappears. In this region, the unit color vector of chiral field plays a defining role, and a gauge field is parametrized in terms of chiral parameters, so that no additional degrees of freedom are introduced by the chiral field. A QCD gauge field decomposition in color bosonization is a sum of a chirally rotated gauge field and an induced axial-vector field expressed in terms of gluonic variables. An induced axial-vector field defines the chiral color anomaly and an effective color action of QCD. This action admits existence of a gauge invariant d=2 condensate of induced axial-vector field and mass.Comment: 13 pages, LaTe

Epidemiological models with parametric heterogeneity: Deterministic theory for closed populations

We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed approach. In particular, we formulate and analyze an SIR model with distributed susceptibility and infectivity, showing that the epidemiological models for closed populations are well suited to the suggested framework. A number of known results from the literature is derived, including the final epidemic size equation for an SIR model with distributed susceptibility. It is proved that the bottom up approach of the theory of heterogeneous populations with parametric heterogeneity allows to infer the population level description, which was previously used without a firm mechanistic basis; in particular, the power law transmission function is shown to be a consequence of the initial gamma distributed susceptibility and infectivity. We discuss how the general theory can be applied to the modeling goals to include the heterogeneous contact population structure and provide analysis of an SI model with heterogeneous contacts. We conclude with a number of open questions and promising directions, where the theory of heterogeneous populations can lead to important simplifications and generalizations.Comment: 26 pages, 6 figures, submitted to Mathematical Modelling of Natural Phenomen