Questions tagged [sine-gordon]
The sine–Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function. This equation attracted a lot of attention in the 1970s due to the presence of soliton solutions. It has importance in quantum field theory, topological aspects like soliton, instanton, in the integrable model, and in exact solutions like Beth ansatz.
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Quantum field in momentum basis for zero-mode of the sine-Gordon model
Given the sine-Gordon model where the boson field $\Phi$ is defined with compactification radius $R$
$$\begin{equation}
\Phi(L) = \Phi(0) + 2\pi Rm, \quad m \in \mathbb{Z}.
\end{equation}\tag{A.6}$$
...
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Physical observables in the XY/sine-Gordon duality
My question is, during the duality map, real physical quantities seem to acquire a prefactor of $i$ and become purely imaginary. And I feel uncomfortable.
Take bosonic current for example. Consider ...
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Energy of moving Sine-Gordon breather
A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation
$$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$)
$$ E = \int_{-\...
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Normal ordering in Sine-Gordon model [duplicate]
I am studying Bosonization from Giamarchi's book (Quantum Physics in 1D), in Appendix E while doing RG analysis at second order he says (Eq. E.18) that we can NOT expand cosine directly because field $...
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Sine-gordon mass term
Simple question: are there some notes or explicit calculations of the mass term from the paper of Zamolodchikov - Mass scale in the sine-gordon model and its reduction (1994)? I need to justify this ...
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Proof that infinite set of conservation laws imply no pair production
In QFT in 1+1 dimensions it is known that the presence of an infinite number of conservation laws, specifically in integrable systems like Sine-Gordon, implies that there is no pair production, and ...
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Can a kink in a finite one dimensional box tunnel into a trivial solution?
Given a simple kink solution of the Sine Gordon equation, is it possible for such a solution in a finite volume to tunnel into a trivial vacuum solution, given that such tunneling demands a finite ...
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Normal-ordering with mass $m$ in sine-Gordon theory
I am new in PSE.
I am studying the $1+1$ sine-Gordon theory from Sidney Coleman's article of 1975 (pdf). The Hamiltonian is
\begin{align}
H=\int dx\;\left(\mathcal{H}_0-\frac{\alpha_0^2}{\beta}\cos\...
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Infinite number of conserved charges for the Sine-Gordon Lagrangian
I recently came across a paper of Witten that talks about the S-matrix of the supersymmetric non-linear sigma model. In the beginning part of the paper, he mentions that theories like the non-linear ...
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Sine Gordon model in 3+1 Dimensions
I'm have read the publication of
Neuenhahn, C. and Marquardt, F. (2015) ‘Quantum simulation of expanding space–time with tunnel-coupled condensates’, New Journal of Physics. IOP Publishing, 17(12), ...
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Asymptotic behaviour of soliton-antisoliton solution for the Sine Gordon equation
The question isn't about any actual homework, it's rather a (probably simple) intermediate step I've encountered on Rajaraman's Solitons and instantons : an introduction to solitons and instantons in ...
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Linear terms in Wilson approach to renormalization
In Wilson's approach to renormalization we break up a field $\phi_0$ which includes modes up to some cutoff $\Lambda$ into two parts, $\phi_0=\phi+\tilde\phi,$ where $\phi$ only has modes up to some ...
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Finding the energy of a solution to the Sine-Gordon equation
I am delving into Quantum-Field Theory, and am stuck trying to work out how to compute the energy of a soliton solution to the Sine-Gordon equation in 1-1 spacetime.
I start with the Lagrangian ...
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Quantum Harmonic Oscillator Matrix Elements
I have a question about the procedure of generating the matrix elements of the Hamiltonian for a Harmonic oscillator.
I understand how to calculate the matrix for the normal Hamiltonian i.e., $$H=\...
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Mathematical content of Thirring/Sine-Gordon duality
I'm a mathematician who is intrigued by the duality between the Thirring and Sine-Gordon models as established by Sidney Coleman.
Can someone explain the mathematical content of this duality to me? (...
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Instanton in sine-Gordon equation
This is a statement from Giamarchi's book on Quantum Physics in 1D:
"For a single-particle in a cosine potential, the slightest amount of
tunneling between two cosine minima leads to conduction ...
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Proof for the Mass gap of sine-Gordon action with $g \cos(\beta \Phi)$
This is the sine-Gordon action:
$$
\frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi
+ g \cos(\beta_{}^{} \cdot\Phi_{})
$$
...
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