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A comment on the path integral approach to cosmological perturbation theory
Get PDFIt is pointed out that the exact renormalization group approach to cosmological perturbation theory, proposed in Matarrese and Pietroni, JCAP 0706 (2007) 026, astro-ph/0703563 and astro-ph/0702653, constitutes a misnomer. Rather, having instructively cast this classical problem into path integral form, the evolution equation then derived comes about as a special case of considering how the generating functional responds to variations of the primordial power spectrum
Dirac-Yang monopoles and their regular counterparts
Get PDFThe Dirac-Yang monopoles are singular Yang–Mills field configurations in all Euclidean dimensions. The regular counterpart of the Dirac monopole in D = 3 is the t Hooft-Polyakov monopole, the former being simply a gauge transform of the asymptotic fields of the latter. Here, regular counterparts of Dirac-Yang monopoles in all dimensions, are described. In the first part of this talk the hierarchy of Dirac–Yang (DY) monopoles will be defined, in the second part the motivation to study these in a topoical context will be briefly presented, and in the last part, two classes of regular counterparts to the DY hierarchy will be presented
The Irish of Iorras Aithneach, County Galway; Volumes I-IV
Get PDFThis grammar is based on extensive fieldwork, published and unpublished lore, and recent as well as older recordings, particularly those held in the archives of Roinn Bhéaloideas Éireann and Raidió na Gaeltachta. These sources provide a picture of extensive variation and change across the six generations born between 1850 and 2000. The grammar draws on several branches of linguistics: descriptive and historical linguistics, dialectology and sociolinguistics. It is the most comprehensive treatment of any variety of Irish.
Volume I provides an introduction and chapters on historical phonology, sandhi and nominal morphology.
Volume II describes plural noun morphology, the verb and pronominals.
Volume III contains chapters on prepositions, functors, initial mutations, higher register, borrowings and language contact, and onomastics.
Volume IV presents transcriptions and a CD containing recordings of a slection of speakers across the generations. The final volume also contains a vocabulary, bibliography and four indexes
Solitons and soliton–antisoliton pairs of a Goldstone model in 3 + 1 dimensions
Get PDFWe study finite energy topologically stable static solutions to a global symmetry breaking model in 3 + 1 dimensions described by an isovector scalar field. The basic features of two different types of configurations are studied, corresponding to axially symmetric multisolitons with topological charge n, and unstable soliton–antisoliton pairs with zero topological charge
Duality in Supersymmetric Yang-Mills and the Quantum Hall effect
Get PDFIt is shown that the long-wavelength, zero-frequency limits of N = 2 supersymmetric Yang-Mills in 3 + 1-dimensions and the quantum Hall effect in 2 + 1 dimensions have many features in common. The phases of both these systems have a hierarchical structure which can be organised and understood in terms of a specific sub-group of the modular group acting on a complex parameter. The complex coupling has positive imaginary part which is the Yang-Mills coupling in the former case and the Ohmic conductivity in the latter. In both case the real part of the complex parameter is associated with a topological term in the effective action for the respective theory. The theoretical scaling flow of SUSY Yang-Mills that follows from modular symmetry is given by a modular form and shows a remarkable similarity to the experimental scaling flow of the quantum Hall effect which, though not necessarily associated with modular forms, is nevertheless strongly constrained by modular symmetry
Determinant solution for the totally asymmetric exclusion process with parallel update
Get PDFWe consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The non-stationary solution of the master equation for the infinite 1D lattice is obtained in a determinant form. Using a modified combinatorial treatment of the Bethe ansatz, we give an alternative derivation of the resulting determinant expression
Modular Symmetry and Fractional Charges in N = 2 Supersymmetric Yang-Mills and the Quantum Hall Effect
Get PDFThe parallel rôles of modular symmetry in N = 2 supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills theories modular symmetry emerges as a version of Dirac’s electric – magnetic duality. It has significant consequences for the vacuum structure of these theories, leading to a fractal vacuum which has an infinite hierarchy of related phases. In the case of N = 2 supersymmetric Yang-Mills in 3+1 dimensions, scaling functions can be defined which are modular forms of a sub-group of the full modular group and which interpolate between vacua. Infra-red fixed points at strong coupling correspond to θ-vacua with θ a rational number that, in the case of pure SUSY Yang-Mills, has odd denominator. There is a mass gap for electrically charged particles which can carry fractional electric charge. A similar structure applies to the 2+1 dimensional quantum Hall effect where the hierarchy of Hall plateaux can be understood in terms of an action of the modular group and the stability of Hall plateaux is due to the fact that odd denominator Hall conductivities are attractive infra-red fixed points. There is a mass gap for electrically charged excitations which, in the case of the fractional quantum Hall effect, carry fractional electric charge
Universality from very general nonperturbative flow equations in QCD
Get PDFIn the context of very general exact renormalization groups, it will be shown that, given a vertex expansion of the Wilsonian effective action, remarkable progress can be made without making any approximations. Working in QCD we will derive, in a manifestly gauge invariant way, an exact diagrammatic expression for the expectation value of an arbitrary gauge invariant operator, in which many of the non-universal details of the setup do not explicitly appear. This provides a new starting point for attacking nonperturbative problems