# 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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### 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? (...
492 views

### 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 ...
31 views

### 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 ...
131 views

### 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 ...
311 views

### Proof for the Mass gap of sine-Gordon action with $g \cos(\beta \Phi)$

This is the sine-Gordon action: $$\frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi + g \cos(\beta_{}^{} \cdot\Phi_{})$$ ...
417 views

### 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 ...
161 views

### 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 ...
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=\...