Approach to a rational rotation number in a piecewise isometric system

We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we prove that in this region the area occupied by stable periodic orbits remains positive. The main device is the construction of an induced map on a domain with vanishing measure; this map is the product of two involutions, and each involution preserves all its atoms. Dynamically, the composition of these involutions represents linking together two sector maps; this dynamical system features an orderly array of stable periodic orbits having a smooth parameter dependence, plus irregular contributions which become negligible in the limit.Comment: LaTeX, 57 pages with 13 figure

Gauge dependence of effective action and renormalization group functions in effective gauge theories

The Caswell-Wilczek analysis on the gauge dependence of the effective action and the renormalization group functions in Yang-Mills theories is generalized to generic, possibly power counting non renormalizable gauge theories. It is shown that the physical coupling constants of the classical theory can be redefined by gauge parameter dependent contributions of higher orders in $\hbar$ in such a way that the effective action depends trivially on the gauge parameters, while suitably defined physical beta functions do not depend on those parameters.Comment: 13 pages Latex file, additional comments in section

Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

Higher-order non-symmetric counterterms in pure Yang-Mills theory

We analyze the restoration of the Slavnov-Taylor (ST) identities for pure massless Yang-Mills theory in the Landau gauge within the BPHZL renormalization scheme with IR regulator. We obtain the most general form of the action-like part of the symmetric regularized action, obeying the relevant ST identities and all other relevant symmetries of the model, to all orders in the loop expansion. We also give a cohomological characterization of the fulfillment of BPHZL IR power-counting criterion, guaranteeing the existence of the limit where the IR regulator goes to zero. The technique analyzed in this paper is needed in the study of the restoration of the ST identities for those models, like the MSSM, where massless particles are present and no invariant regularization scheme is known to preserve the full set of ST identities of the theory.Comment: Final version published in the journa

Exact solution (by algebraic methods) of the lattice Schwinger model in the strong-coupling regime

Using the monomer--dimer representation of the lattice Schwinger model, with $N_f =1$ Wilson fermions in the strong--coupling regime ($\beta=0$), we evaluate its partition function, $Z$, exactly on finite lattices. By studying the zeroes of $Z(k)$ in the complex plane $(Re(k),Im(k))$ for a large number of small lattices, we find the zeroes closest to the real axis for infinite stripes in temporal direction and spatial extent $S=2$ and 3. We find evidence for the existence of a critical value for the hopping parameter in the thermodynamic limit $S\rightarrow \infty$ on the real axis at about $k_c \simeq 0.39$. By looking at the behaviour of quantities, such as the chiral condensate, the chiral susceptibility and the third derivative of $Z$ with respect to $1/2k$, close to the critical point $k_c$, we find some indications for a continuous phase transition.Comment: 22 pages (6 figures

Hyperbolic outer billiards : a first example

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.Comment: 11 pages, 8 figures, to appear in Nonlinearit

Jorge A. Swieca's contributions to quantum field theory in the 60s and 70s and their relevance in present research

After revisiting some high points of particle physics and QFT of the two decades from 1960 to 1980, I comment on the work by Jorge Andre Swieca. I explain how it fits into the quantum field theory during these two decades and draw attention to its relevance to the ongoing particle physics research. A particular aim of this article is to direct thr readers mindfulness to the relevance of what at the time of Swieca was called "the Schwinger Higgs screening mechanism". which, together with recent ideas which generalize the concept of gauge theories, has all the ingredients to revolutionize the issue of gauge theories and the standard model.Comment: 49 pages, expansion and actualization of text, improvement of formulations and addition of many references to be published in EPJH - Historical Perspectives on Contemporary Physic

The General Correlation Function in the Schwinger Model on a Torus

In the framework of the Euclidean path integral approach we derive the exact formula for the general N-point chiral densities correlator in the Schwinger model on a torusComment: 17 pages, misprints corrected, references adde

Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen

Renormalization Group Study of Chern-Simons Field Coupled to Scalar Matter in a Modified BPHZ Subtraction Scheme

We apply a soft version of the BPHZ subtraction scheme to the computation of two-loop corrections from an Abelian Chern-Simons field coupled to (massive) scalar matter with a $\lambda(\Phi^\dag\Phi)^2$ and $\nu(\Phi^\dag\Phi)^3$ self-interactions. The two-loop renormalization group functions are calculated. We compare our results with those in the literature.Comment: 15 pages, 7 figures, revtex. To appear in Phys. Rev.