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Algebraic structure of classical integrability for complex sine-Gordon
by J. Avan, L. Frappat, E. Ragoucy
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Luc FRAPPAT |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1911.06720v2 (pdf) |
| Date accepted: | 2020-02-11 |
| Date submitted: | 2020-01-30 01:00 |
| Submitted by: | FRAPPAT, Luc |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified classical reflection/Yang--Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra $su(2)^*$. The sign shift pattern of this deformation has the signature of the twisted boundary dynamical algebra. Issues related to the quantization of this algebraic structure and the formulation of quantum complex sine-Gordon on those lines are introduced and discussed.
List of changes
Dear Editor,
We have revised our manuscript according to the requested changes of the referee. Here are the major modifications:
- page 2, the sentence has been modified to clarify the point.
- we added three paragraphs in section 3 :
a/ page 8, a comment on an alternative procedure of quantizing the complex sine-Gordon model (with refs 23 and 24 added);
b/ page 8, a comment on the potential existence of discrete quantum systems related to CSG (with ref. 26).
c/ page 9, a final paragraph about the feasibility of the quantization itself.
In addition, the grammar and the punctuation have been revised.
Best regards,
The authors
Published as SciPost Phys. 8, 033 (2020)