14 Jun 2017 The sine-Gordon model will play an important role in layered Then, the Lagrangian is written by means of renormalized field and constants.

We present the dimensional regularization approach to the renormalization group theory of the generalized sine-Gordon model. The generalized sine-Gordon model means the sine-Gordon model with high frequency cosine modes. We derive renormalization group equations for the generalized sine-Gordon model by regularizing the divergence based on the dimensional method. We discuss the scaling property

The two-dimensional (2D) sine-Gordon model describes the Kosterlitz-Thouless transition of the 2D classical XY model [5,6]. The 2D sine-Gordon model is mapped to the … 2019-03-18 sine-Gordon theory and a one-parameter deformation of the O(3) sigma model, the sausage model. This allows us to write down a free eld representation for the Zamolodchikov-Fateev algebra of the sausage model and to construct an integral representation for the … The name "sine-Gordon equation" is a pun on the well-known Klein–Gordon equation in physics: φ t t − φ x x + φ = 0. {\displaystyle \varphi _{tt}-\varphi _{xx}+\varphi \ =0.\,} The sine-Gordon equation is the Euler–Lagrange equation of the field whose Lagrangian density is given by The sine-Gordon equation is the Euler–Lagrange equation for this Lagrangian.

Let us consider the linear Klein-Gordon equation, which describes based on using a trial function in the Lagrangian for the sine-Gordon equation. The effect of the shed dispersive ra- diation on the evolving soliton is determined 15 May 1993 k+ =(k +k')/&2 —+0. After canonically quantizing the effective Lagrangian, one obtains the effective light-front Hamiltonian which agrees with the 30 Jul 1985 Generating equations for the nonlinear Schrodinger equation and the sine- Gordon equation. Here we construct generating equation for NSE. Variational symmetries and closedness of multi-time Lagrangian forms . .

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quantitative conclusions. The Lagrangian under consideration is L() - ^{|ф2-с 0 2ф х 2-« р 2(1-совф) ) +ееф (1) where the first term represents the sine-Gordon equation for the field ф, and the second one describes the effect of an external field e. The parameters N 0, o 0, u^, e* may be of different micro

The. U(1) gauge theory is nothing but two-gap superconductors or chiral p-wave super- 1995-12-06 The sine-Gordon equation may be derived from the Lagrangian: (1.2) L = Z dx 1 2 ˚2 t − 1 2 ˚2 x +cos˚−1 ; 2000 Mathematics Subject Classi cation. Primary: 35J20, 58E05; Secondary: 35Q20, 65N30. Key words and phrases. Elliptic sine-Gordon equation, variational methods, numerical computation.

This method is based on using a solitonlike pulse with variable parameters in an averaged Lagrangian for the sine-Gordon equation. This averaged Lagrangian

(4) To produce a pulse with a sharp front, it is now assumed that 0 < 1. Lecture 1: sine-Gordon equation and solutions • Equivalent circuit • Derivation of sine-Gordon equation • The most important solutions plasma waves a soliton! chain of solitons resistive state breather and friends • Mechanical analog: the chain of pendula • Penetration of magnetic ﬁeld Introduction to the ﬂuxon dynamics in LJJ Nr. 2 Equation (6.56) is identical to the sine–Gordon equation used to describe commensurate-incommensurate transitions in solids, for which structural configurations correspond to minima of the effective potential V [4].For the purposes of the current discussion, we will neglect the q–dependence of δ and assume that it is fixed.We note, however, that it is possible for δ to become negative as 1996-02-01 The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim $\sigma$-models, and they are integrable exhibiting a black-hole type 2021-03-16 Lagrangian. In Section 3, sine-Gordon kinks with a modiﬁed mass term and their non-Abelian. U(N) generalization are discussed. In Section 4, these sine-Gordon kinks are promoted to gauge theories. The. U(1) gauge theory is nothing but two-gap superconductors or chiral p-wave super- 1995-12-06 The sine-Gordon equation may be derived from the Lagrangian: (1.2) L = Z dx 1 2 ˚2 t − 1 2 ˚2 x +cos˚−1 ; 2000 Mathematics Subject Classi cation.

(4) To produce a pulse with a sharp front, it is now assumed that 0 < 1.
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In Section 3, sine-Gordon kinks with a modiﬁed mass term and their non-Abelian. U(N) generalization are discussed. In Section 4, these sine-Gordon kinks are promoted to gauge theories.

The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim $\sigma$-models, and they are integrable exhibiting a black-hole type one-dimensional soliton solution of the Sine-Gordon equation. An averaged Lagrangian is now calculated by substituting the approximate solution (3) into the Lagrangian (2) and integrating over all space. The averaged Lagrangian L is then L = 2π 0 ∞ 0 Lrdrdθ.
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to Sine-Gordon, Z2 + periodic −→ topological β2 Complete Lagrangian for the Higgs sector. L = 1. Klein-Gordon and Sine-Gordon equation and consider the hamiltonian.

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Infinite number of conserved charges for the Sine-Gordon Lagrangian. Ask Question Asked 1 year, 3 months ago. Active 1 year, 3 months ago. Viewed 61 times 4. 5 $\begingroup$ I recently came across a paper of Witten that talks about the S-matrix of the supersymmetric non-linear sigma model. In the

oändliga-dimensionella Hamiltonian-system (både klassiska och kvanta) och den År 1973 hade hans forskargrupp i UMIST hittat lösningar på sinus-Gordon och Polynomial conserved densities for sine-Gordon equations Proceedings of av T Ohlsson · Citerat av 1 — presence of Yukawa coupling terms for these particles in the Lagrangian (1.4); but @t2 (x;t). The Klein{Gordon equation does not reveal the full spin.

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In Section 4, these sine-Gordon kinks are promoted to gauge theories The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim σ-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F ⊃ G ⊃ H. The canonical sine-Gordon Lagrangian is replaced by an effective Lagrangian which does not lead to divergences as k + =(k 0 +k 1)/ √2 -->0. After canonically quantizing the effective Lagrangian, one obtains the effective light-front Hamiltonian which agrees with the naive light-front (LF) Hamiltonian, up to one additional renormalization. The Klein–Gordon equation does not form the basis of a consistent quantum relativistic one-particle theory. There is no known such theory for particles of any spin. For full reconciliation of quantum mechanics with special relativity, quantum field theory is needed, in which the Klein–Gordon equation reemerges as the equation obeyed by the components of all free quantum fields.

Elliptic sine-Gordon equation, variational methods, numerical computation.