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

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

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

Theoretical implications of the second time derivative of the period of the pulsar NP0532

Theoretical implications of second time derivative with existing magnetic dipole model

The Hierarchy Principle and the Large Mass Limit of the Linear Sigma Model

In perturbation theory we study the matching in four dimensions between the linear sigma model in the large mass limit and the renormalized nonlinear sigma model in the recently proposed flat connection formalism. We consider both the chiral limit and the strong coupling limit of the linear sigma model. Our formalism extends to Green functions with an arbitrary number of pion legs,at one loop level,on the basis of the hierarchy as an efficient unifying principle that governs both limits. While the chiral limit is straightforward, the matching in the strong coupling limit requires careful use of the normalization conditions of the linear theory, in order to exploit the functional equation and the complete set of local solutions of its linearized form.Comment: Latex, 41 pages, corrected typos, final version accepted by IJT

One-loop Self-energy and Counterterms in a Massive Yang-Mills Theory based on the Nonlinearly Realized Gauge Group

In this paper we evaluate the self-energy of the vector mesons at one loop in our recently proposed subtraction scheme for massive nonlinearly realized SU(2) Yang-Mills theory. We check the fulfillment of physical unitarity. The resulting self-mass can be compared with the value obtained in the massive Yang-Mills theory based on the Higgs mechanism, consisting in extra terms due to the presence of the Higgs boson (tadpoles included). Moreover we evaluate all the one-loop counterterms necessary for the next order calculations. By construction they satisfy all the equations of the model (Slavnov-Taylor, local functional equation and Landau gauge equation). They are sufficient to make all the one-loop amplitudes finite through the hierarchy encoded in the local functional equation.Comment: 26 pages, 12 figures, minor changes, final version accepted by Phys. Rev. D, typos corrected in eqs.(8),(17),(27),(28

Competition interfaces and second class particles

The one-dimensional nearest-neighbor totally asymmetric simple exclusion process can be constructed in the same space as a last-passage percolation model in Z^2. We show that the trajectory of a second class particle in the exclusion process can be linearly mapped into the competition interface between two growing clusters in the last-passage percolation model. Using technology built up for geodesics in percolation, we show that the competition interface converges almost surely to an asymptotic random direction. As a consequence we get a new proof for the strong law of large numbers for the second class particle in the rarefaction fan and describe the distribution of the asymptotic angle of the competition interface.Comment: Published at http://dx.doi.org/10.1214/009117905000000080 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Decoupling of the longitudinal polarization of the vector field in the massless Higgs-Kibble model

It is shown that the three dimensionally longitudinal component of the vector field decouples in the massless limit of nonabelian Higgs model.Comment: 6 pages, no figure