Analysis of a method for precisely relating a seafloor point to a distant point on land

A study of the environmental constraints and engineering aspects of the acoustic portion of a system for making geodetic ties between undersea reference points and others on land is described. Important areas in which to make such observations initially would be from the California mainland out to oceanic points seaward of the San Andreas fault, and across the Aleutian Trench. The overall approach would be to operate a GPS receiver in a relative positioning (interferometric) mode to provide the long range element of the baseline determination (10 to 1,000 km) and an array of precision sea floor acoustic transponders to link the locally moving sea surface GPS antenna location to a fixed sea floor point. Analyses of various environmental constrants (tides, waves, currents, sound velocity variations) lead to the conclusion that, if one uses a properly designed transponder having a remotely controllable precise retransmission time delay, and is careful with regard to methods for installing these on the sea floor, one should, in many ocean locations, be able to achieve sub-decimeter overall system accuracy. Achievements of cm accuracy or better will require additional understanding of time and space scales of variation of sound velocity structure in the ocean at relevant locations

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

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

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

Gauge Consistent Wilson Renormalization Group I: Abelian Case

A version of the Wilson Renormalization Group Equation consistent with gauge symmetry is presented. A perturbative renormalizability proof is established. A wilsonian derivation of the Callan-Symanzik equation is given.Comment: Latex2e, 39 pages, 3 eps figures. Revised version to appear in Int. J. Mod. Phy

Dynamical Breakdown of Symmetry in a (2+1) Dimensional Model Containing the Chern-Simons Field

We study the vacuum stability of a model of massless scalar and fermionic fields minimally coupled to a Chern-Simons field. The classical Lagrangian only involves dimensionless parameters, and the model can be thought as a (2+1) dimensional analog of the Coleman-Weinberg model. By calculating the effective potential, we show that dynamical symmetry breakdown occurs in the two-loop approximation. The vacuum becomes asymmetric and mass generation, for the boson and fermion fields takes place. Renormalization group arguments are used to clarify some aspects of the solution.Comment: Minor modifications in the text and figure