B. K. Chung

Renormalization group improvement of the effective potential in massive {phi}{sup 4} theory

The renormalization group method is applied to the three-loop effective potential of the massive φ4 theory in the MS scheme in order to obtain the next-next-next-to leading logarithm resummation. For this, we use already known four-loop renormalization group functions and calculate perturbatively evolutions of the parameters (λ, m2, φ and, Λ) along the running scale within the accuracy of the three-loop order. We also comment on the structure of five-loop effective potential using the renormalization group equation for the effective potential and the existing five-loop renormalization group functions. PACS number(s): 11.10.Hi Typeset using REVTEX ∗Electronic address: chung@ctpred.mit.edu †Electronic address: bkchung@nms.kyunghee.ac.kr

Calculation of a class of three loop vacuum diagrams with two different mass values

Using the method of Chetyrkin, Misiak, and M{umlt u}nz we calculate analytically a class of three-loop vacuum diagrams with two different mass values, one of which is one-third as large as the other. In particular, this specific mass ratio is of great interest in relation to the three-loop effective potential of the O(N) {phi}{sup 4} theory. All pole terms in {epsilon}=4{minus}D (D being the space-time dimensions in a dimensional regularization scheme) plus finite terms containing the logarithm of mass are kept in our calculation of each diagram. It is shown that a three-loop effective potential calculated using the three-loop integrals obtained in this paper agrees, in the large-N limit, with the overlap part of the leading-order (in the large-N limit) calculation of Coleman, Jackiw, and Politzer [Phys. Rev. D {bold 10}, 2491 (1974)]. {copyright} {ital 1999} {ital The American Physical Society}

Conformal turbulence with boundary

Abstract Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum confined in the upper half plane are obtained using the image method. This result enables us to address the infrared problem of the theory of conformal turbulence.

Solutions of conformal turbulence on a half plane

Abstract Exact solutions of conformal turbulence restricted to the upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorovs solution consistently and differ from the Polyakovs bulk case which requires a fine tuning of coefficients. The simplest solution in our case is given by the minimal model of p = 2, q = 33 and moreover we find a fixed point of solutions when p , q become large.

Possible tests of conformal turbulence through boundaries

Abstract We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal transformations, or insert boundary operators so as to handle more general cases. Effects of such operations will be reflected in physically measurable quantities such as the energy power spectrum E ( k ) or the average velocity profiles. We propose that these effects can be used as a possible test of conformal turbulence in an experimental setting. We also study the periodic boundary conditions, i.e. turbulence on a torus geometry. The dependence of moduli parameter q appears explicitly in the one point functions in the theory, which can also be tested.

Yang–Baxter Systems, Nonlinear Models and Their Applications: Proceedings of the APCTP–Nankai Symposium

Solvable models in statistical mechanics - from Ising to Chiral Potts, R.J. Baxter functional integration and the Kontsevich integral, L.H. Kauffman some applications of exactly solved models in statistical mechanics, M.T. Batchelor edge states tunnelling in the fractional quantum Hall effect - physical and mathematical applications of integrability, H. Saleur boundary flows in general coset theories, C. Ahn avoided strings in bacterial complete genomes and a related combinatorical problem, B.L. Hao self-dual polynomials in statistical physics and number theory, F.Y. Wu stable membranes in the Weinberg-Salam model? A.J. Niemi et al description of the Bose-Einstein condensate state, A.I. Solomon et al nonlinear analysis of the Bose-Einstein condensates, M. Wadati and T. Tsurumi a Hubbard model with pair hopping and on universal dynamical R-matrices, D. Arnaudon quasi-Hopf twistors for elliptic quantum groups, S. Odake classification of commuting differential operators with two variables, H. Ochiai. (Part contents)

HAMILTONIAN FORMULATION OF SL(3) Ur-KdV EQUATION

We give a unified view of the relation between the SL(2) KdV, the mKdV, and the Ur-KdV equations through the Frechet derivatives and their inverses. For this we introduce a new procedure of obtaining the Ur-KdV equation, where we require that it has no nonlocal operators. We extend this method to the SL(3) KdV equation, i.e. Boussinesq (Bsq) equation and obtain the Hamiltonian structure of Ur-Bsq .equation in a simple form. In particular, we explicitly construct the Hamiltonian operator of the Ur-Bsq system which defines the Poisson structure of the system, through the Frechet derivative and its inverse.