Renormalization trasformations of the 4D BFYM theory

We study the most general renormalization transformations for the first-order formulation of the Yang-Mills theory. We analyze, in particular, the trivial sector of the BRST cohomology of two possible formulations of the model: the standard one and the extended one. The latter is a promising starting point for the interpretation of the Yang-Mills theory as a deformation of the topological BF theory. This work is a necessary preliminary step towards any perturbative calculation, and completes some recently obtained results.Comment: 12 pages, Late

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

Axial Anomaly from the BPHZ regularized BV master equation

A BPHZ renormalized form for the master equation of the field antifiled (or BV) quantization has recently been proposed by De Jonghe, Paris and Troost. This framework was shown to be very powerful in calculating gauge anomalies. We show here that this equation can also be applied in order to calculate a global anomaly (anomalous divergence of a classically conserved Noether current), considering the case of QED. This way, the fundamental result about the anomalous contribution to the Axial Ward identity in standard QED (where there is no gauge anomaly) is reproduced in this BPHZ regularized BV framework.Comment: 10 pages, Latex, minor changes in the reference

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

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

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

Stickiness in Hamiltonian systems: from sharply divided to hierarchical phase space

We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with non-hierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one-parameter families of marginally unstable periodic orbits and is characterized by an exponent \gamma= 2 for the asymptotic power-law decay of the distribution of recurrence times. Generic perturbations lead to systems with hierarchical phase space, where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and Cantori. In this case, we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power-laws, depending on the relative contribution of the primary and secondary structures of the hierarchy. Numerical verification of our main results are provided for area-preserving maps, mushroom billiards, and the newly defined magnetic mushroom billiards.Comment: To appear in Phys. Rev. E. A PDF version with higher resolution figures is available at http://www.pks.mpg.de/~edugal

Study of Quark Propagator Solutions to the Dyson--Schwinger Equation in a Confining Model

We solve the Dyson--Schwinger equation for the quark propagator in a model with singular infrared behavior for the gluon propagator. We require that the solutions, easily found in configuration space, be tempered distributions and thus have Fourier transforms. This severely limits the boundary conditions that the solutions may satisify. The sign of the dimensionful parameter that characterizes the model gluon propagator can be either positive or negative. If the sign is negative, we find a unique solution. It is singular at the origin in momentum space, falls off like $1/p^2$ as $p^2\rightarrow +/-\infty$, and it is truly nonperturbative in that it is singular in the limit that the gluon--quark interaction approaches zero. If the sign of the gluon propagator coefficient is positive, we find solutions that are, in a sense that we exhibit, unconstrained linear combinations of advanced and retarded propagators. These solutions are singular at the origin in momentum space, fall off like $1/p^2$ asympotically, exhibit ``resonant--like" behavior at the position of the bare mass of the quark when the mass is large compared to the dimensionful interaction parameter in the gluon propagator model, and smoothly approach a linear combination of free--quark, advanced and retarded two--point functions in the limit that the interaction approaches zero. In this sense, these solutions behave in an increasingly ``particle--like" manner as the quark becomes heavy. The Feynman propagator and the Wightman function are not tempered distributions and therefore are not acceptable solutions to the Schwinger--Dyson equation in our model. On this basis we advance several arguments to show that the Fourier--transformable solutions we find are consistent with quark confinement, even though they have singularities on th

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