Renormalization of the Non-Linear Sigma Model in Four Dimensions. A two-loop example

The renormalization procedure of the non-linear SU(2) sigma model in D=4 proposed in hep-th/0504023 and hep-th/0506220 is here tested in a truly non-trivial case where the non-linearity of the functional equation is crucial. The simplest example, where the non-linear term contributes, is given by the two-loop amplitude involving the insertion of two \phi_0 (the constraint of the non-linear sigma model) and two flat connections. In this case we verify the validity of the renormalization procedure: the recursive subtraction of the pole parts at D=4 yields amplitudes that satisfy the defining functional equation. As a by-product we give a formal proof that in D dimensions (without counterterms) the Feynman rules provide a perturbative symmetric solution.Comment: Latex, 3 figures, 19 page

Wannier functions and Fractional Quantum Hall Effect

We introduce and study the Wannier functions for an electron moving in a plane under the influence of a perpendicular uniform and constant magnetic field. The relevance for the Fractional Quantum Hall Effect is discussed; in particular it shown that an interesting Hartree-Fock state can be constructed in terms of Wannier functions.Comment: 7 pages, RevTeX 3.0, 5 tar-compressed and uu-encoded figure

The SU(2) X U(1) Electroweak Model based on the Nonlinearly Realized Gauge Group

The electroweak model is formulated on the nonlinearly realized gauge group SU(2) X U(1). This implies that in perturbation theory no Higgs field is present. The paper provides the effective action at the tree level, the Slavnov Taylor identity (necessary for the proof of unitarity), the local functional equation (used for the control of the amplitudes involving the Goldstone bosons) and the subtraction procedure (nonstandard, since the theory is not power-counting renormalizable). Particular attention is devoted to the number of independent parameters relevant for the vector mesons; in fact there is the possibility of introducing two mass parameters. With this choice the relation between the ratio of the intermediate vector meson masses and the Weinberg angle depends on an extra free parameter. We briefly outline a method for dealing with \gamma_5 in dimensional regularization. The model is formulated in the Landau gauge for sake of simplicity and conciseness: the QED Ward identity has a simple and intriguing form.Comment: 19 pages, final version published by Int. J. Mod. Phys. A, some typos corrected in eqs.(1) and (41). The errors have a pure editing origin. Therefore they do not affect the content of the pape

Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure

In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are relevant from the perspective of stochastic growth models, in particular: (a) the surface fluctuations are asymptotically Gaussian on a sqrt(ln(t)) scale and (b) the correlation structure of the surface is asymptotically given by the massless field.Comment: 13 pages, 4 figure

Particle tracking in the ILC extraction lines with DIMAD and BDSIM

The study of beam transport is of central importance to the design and performance assessment of modern particle accelerators. In this paper, we benchmark two contemporary codes, DIMAD and BDSIM, the latter being a relatively new tracking code built within the framework of GEANT4. We consider both the 20 mrad and 2 mrad extraction lines of the 500 GeV International Linear Collider (ILC) and we perform particle tracking studies of heavily disrupted post-collision electron beams. We find that the two codes give an almost equivalent description of the beam transport

Path-integral over non-linearly realized groups and Hierarchy solutions

The technical problem of deriving the full Green functions of the elementary pion fields of the nonlinear sigma model in terms of ancestor amplitudes involving only the flat connection and the nonlinear sigma model constraint is a very complex task. In this paper we solve this problem by integrating, order by order in the perturbative loop expansion, the local functional equation derived from the invariance of the SU(2) Haar measure under local left multiplication. This yields the perturbative definition of the path-integral over the non-linearly realized SU(2) group.Comment: 26 page

Benchmarking of Tracking Codes (BDSIM/DIMAD) using the ILC Extraction Lines

The study of beam transport is of central importance to the design and performance assessment of modern particle accelerators. In this work, we benchmark two contemporary codes - DIMAD and BDSIM, the latter being a relatively new tracking code built within the framework of GEANT4. We consider both the 20 mrad and 2 mrad extraction lines of the International Linear Collider (ILC) and we perform tracking studies of heavily disrupted post-collision electron beams. We find that the two codes mostly give an equivalent description of the beam transport.Comment: Contribution to the Tenth European Particle Accelerator Conference `"EPAC'06'', Edinburgh, United-Kingdom, 26-30 June 200

Spatial birth-and-death processes in random environment

We consider birth-and-death processes of objects (animals) defined in ${\bf Z}^d$ having unit death rates and random birth rates. For animals with uniformly bounded diameter we establish conditions on the rate distribution under which the following holds for almost all realizations of the birth rates: (i) the process is ergodic with at worst power-law time mixing; (ii) the unique invariant measure has exponential decay of (spatial) correlations; (iii) there exists a perfect-simulation algorithm for the invariant measure. The results are obtained by first dominating the process by a backwards oriented percolation model, and then using a multiscale analysis due to Klein to establish conditions for the absence of percolation.Comment: 48 page

Numerical analysis of the master equation

Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme that remains stable with much larger time increments than can be used in standard methods. When only the stationary distribution is required, a direct iteration method is even more rapid; this method may be extended to construct the quasi-stationary distribution of a process with an absorbing state. Applications to birth-and-death processes reveal gains in efficiency of two or more orders of magnitude.Comment: 7 pages 3 figure