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B. K. Chung

Publications and source records attributed to B. K. Chung.

15 recordsLinked to original sources
arXiv2002

Evaluation of a Class of Two-Scale Three-Loop Vacuum Diagrams

As a generalization of a previous work [Phys. Rev. D. {\bf 59}, 105014 (1999)], we compute analytically a class of three-loop vacuum diagrams with two {\em arbitrarily} different mass scales. We use a decomposition algorithm in which the integrand of the final integral for the third momentum vector, say, $k$, becomes independent of the angles of $k$-vector in spherical polar coordinates. This algorithm proves to be very efficient in obtaining exclusively all $\e$-pole terms of the given diagram.

hep-ph↗
arXiv2002

RG-Improved Three-Loop Effective Potential of the Massive $ϕ^4$ theory

The renormalization group method is applied to the three-loop effective potential of the massive $ϕ^4$ theory in the $\bar{\rm MS}$ scheme in order to obtain the next-next-next-to-leading logarithm resummation. For this, we exploit four-loop parts of the renormalization group functions $β_λ$, $γ_m$, $γ_ϕ$, and $β_Λ$, which were already given to five-loop order via the renormalization of the zero-, two-, and four-point one-particle-irreducible Green's functions, to solve evolution equations for the parameters $λ$, $m^2$, $ϕ$, and $Λ$ within the accuracy of the three-loop order.

hep-th↗
arXiv2001

Reduction of a Class of Three-Loop Vacuum Diagrams to Tetrahedron Topologies

We obtain finite parts (as well as $ε$-pole parts) of massive three-loop vacuum diagrams with three-point and/or four-point interaction vertices by reducing them to tetrahedron diagrams with both massive and massless lines, whose finite parts were given analytically in a recent paper by Broadhurst. In the procedure of reduction, the method of integration-by-parts recurrence relations is employed. We use our result to compute the $\bar{\rm MS}$ effective potential of the massive $ϕ^4$ theory.

hep-th↗
arXiv2001

Induced Lorentz- and CPT-violating Chern-Simons term in QED: Fock-Schwinger proper time method

Using the Fock-Schwinger proper time method, we calculate the induced Chern-Simons term arising from the Lorentz- and CPT-violating sector of quantum electrodynamics with a $b_μ\barψγ^μγ_5 ψ$ term. Our result to all orders in $b$ coincides with a recent linear-in-$b$ calculation by Chaichian et al. [hep-th/0010129 v2]. The coincidence was pointed out by Chung [Phys. Lett. {\bf B461} (1999) 138] and Pérez-Victoria [Phys. Rev. Lett. {\bf 83} (1999) 2518] in the standard Feynman diagram calculation with the nonperturbative-in-$b$ propagator.

hep-th↗
arXiv1999

Calculation of a Class of Three-Loop Vacuum Diagrams with Two Different Mass Values

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, using the method of Chetyrkin, Misiak, and Münz in the dimensional regularization scheme. All pole terms in ε=4-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 three-loop effective potential calculated using three-loop integrals obtained in this paper agrees, in the large-N limit, with the overlap part of leading-order (in the large-N limit) calculation of Coleman, Jackiw, and Politzer [Phys. Rev. D {\bf 10}, 2491 (1974)].

hep-ph↗
arXiv1998

Three-Loop Effective Potential of O(N) $ϕ^4$ Theory

The three-loop effective potential of the massless O(N) $ϕ^4$ theory is calculated analytically using techniques of dimensional regularization. We see a complete agreement between our result and Jackiw's result obtained only up to two-loop order using a different regularization (cutoff regularization) method, but the same renormalization conditions. For an easy check of the mutual cancellation of all the dangerous pole terms in each loop order, we give the $ε$-expanded loop integrals in full detail.

hep-ph↗
arXiv1994

An Effective Action for Quasi-elastic Scatterings in QCD

A new effective action for the high energy quark-quark scatterings is obtained by applying a scaling approximation to the QCD action. The propagators are shown to factorize into the transverse and the longitudinal parts so that the scattering amplitudes are given in terms of the products of two dimensional $S$-matrices. we show that our action provides a natural effective field theory for the Lipatov's theory of quark scatterings with quasi-elastic unitarity. The amplitude with quasi-elastic unitarity obtained from this action shows `Regge' behavior and is eikonalized.

hep-th↗
arXiv1994

Spontaneous Breaking of Parity in 2+1-Dimensional Thirring Model

A new aspect of the vacuum structure of 2+1-dimensional Thirring model is presented. Using the Fierz identity, we split the current-current four-Fermi interaction in terms of a matrix valued auxiliary scalar field and compute its effective potential. Energy consideration shows that contrary to earlier expectations, parity in general is spontaneously broken at any finite order of N, where N is the number of the two component spinors. In the large N limit, there does not exist a stable vacuum of the theory thereby making the application of the large N limit to Thirring model dangerous. A detailed analysis for parity breaking solutions in N=2,3 cases is given.

hep-th↗
arXiv1993

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 Fréchet derivatives and their inverses. For this we introduce a new procedure of obtaining the Ur-KdV equation, where we require that it has no non-local operators. We extend this method to the $SL(3)$ KdV equation, i.e., Boussinesq(Bsq) equation and obtain the hamiltonian structure of Ur-Bsq equationin 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 Fréchet derivative and its inverse.

hep-th↗
arXiv1993

Possible Tests of Conformal Turbulence through Boundaries

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 explictly in the one point functions in the theory, which can also be tested.

hep-th↗
arXiv1993

Solutions of Conformal Turbulence on a Half Plane

Exact solutions of conformal turbulence restricted on a 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 Kolmogorov's solution consistently and differ from the Polyakov's bulk case which requires a fine tunning 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.

hep-th↗
arXiv1993

Classical $W_3^{(2)}$ algebra and its Miura map

We verify that the fractional KdV equation is a bi-hamiltonian system using the zero curvature equation in $SL(3)$ matrix valued Lax pair representation, and explicitly find the closed form for the hamiltonian operators of the system. The second hamiltonian operator is the classical version of the $W^{(2)}_3$ algebra. We also construct systematically the Miura map of $W^{(2)}_3$ algebra using a gauge transformation of the $SL(3)$ matrix valued Lax operator in a particular gauge, and construct the modified fractional KdV equaiotn as hamiltonian system.

hep-th↗
arXiv1993

Conformal Turbulence with Boundary

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.

hep-th↗