32 research outputs found

    Renormalization of composite operators

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    The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the ϕ3\phi^3 theory in dimension d=6d=6.Comment: 24 pages, revtex (accepted by Phys. Rev. D), changes in introduction and summar

    Endowing the Nonlinear Sigma Model with a Flat Connection Structure: a Way to Renormalization

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    We discuss the quantized theory of a pure-gauge non-abelian vector field (flat connection) as it would appear in a mass term a` la Stueckelberg. However the paper is limited to the case where only the flat connection is present (no field strength term). The perturbative solution is constructed by using only the functional equations and by expanding in the number of loops. In particular we do not use a perturbative approach based on the path integral or on a canonical quantization. It is shown that there is no solution with trivial S-matrix. Then the model is embedded in a nonlinear sigma model. The solution is constructed by exploiting a natural hierarchy in the functional equations given by the number of insertions of the flat connection and of the constrained component of the sigma field. The amplitudes with the sigma field are simply derived from those of the flat connection and of the constraint component. Unitarity is enforced by hand by using Feynman rules. We demonstrate the remarkable fact that in generic dimensions the naive Feynman rules yield amplitudes that satisfy the functional equations. This allows a dimensional renormalization of the theory in D=4 by recursive subtractions of the poles in the Laurent expansion. Thus one gets a finite theory depending only on two parameters. The novelty of the paper is the use of the functional equation associated to the local left multiplication introduced by Faddeev and Slavnov, here improved by adding the external source coupled to the constrained component. It gives a powerful tool to renormalize the nonlinear sigma model.Comment: 42 pages, 7 figures, Latex; improved presentation of the subtraction procedur

    Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics

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    When Lenz proposed a simple model for phase transitions in magnetism, he couldn't have imagined that the "Ising model" was to become a jewel in field of equilibrium statistical mechanics. Its role spans the spectrum, from a good pedagogical example to a universality class in critical phenomena. A quarter century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing a seemingly trivial modification to the Ising lattice gas, they took it into the vast realms of non-equilibrium statistical mechanics. An abundant variety of unexpected behavior emerged and caught many of us by surprise. We present a brief review of some of the new insights garnered and some of the outstanding puzzles, as well as speculate on the model's role in the future of non-equilibrium statistical physics.Comment: 3 figures. Proceedings of 100th Statistical Mechanics Meeting, Rutgers, NJ (December, 2008

    EC85-219 1985 Nebraska Swine Report

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    This 1985 Nebraska Swine Report was prepared by the staff in Animal Science and cooperating departments for use in the Extension and Teaching programs at the University of Nebraska-Lincoln. Authors from the following areas contributed to this publication: Swine Nutrition, swine diseases, pathology, economics, engineering, swine breeding, meats, agronomy, and diagnostic laboratory. It covers the following areas: breeding, disease control, feeding, nutrition, economics, housing and meats

    Field Theory Approaches to Nonequilibrium Dynamics

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    It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale invariance, both near and far from thermal equilibrium. Part 1 introduces the response functional field theory representation of (nonlinear) Langevin equations. The RG is employed to compute the scaling exponents for several universality classes governing the critical dynamics near second-order phase transitions in equilibrium. The effects of reversible mode-coupling terms, quenching from random initial conditions to the critical point, and violating the detailed balance constraints are briefly discussed. It is shown how the same formalism can be applied to nonequilibrium systems such as driven diffusive lattice gases. Part 2 describes how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then used to analyse simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterised by the power laws of (critical) directed percolation. Certain other important universality classes are mentioned, and some open issues are listed.Comment: 54 pages, 9 figures, Lecture Notes for Luxembourg Summer School "Ageing and the Glass Transition", submitted to Springer Lecture Notes in Physics (www.springeronline/com/series/5304/

    Renormalization group flows and continual Lie algebras

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    We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z_n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.Comment: latex, 73pp including 14 eps fig
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