# 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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### 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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### 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: $$\frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi + g \cos(\beta_{}^{} \cdot\Phi_{})$$ ...