Aspects of Integrable Defects

Ed Corrigan

Aspects of Integrable Defects

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Defects and impurities are ubiquitous in nature and essential for the understanding of phenomena in many domains of physics ranging from classical continuum mechanics to condensed matter physics, or cosmology. In every case, a defect is likely to be modeled by a discontinuity in a field variable, such as the abrupt change in fluid velocity across a shock, or the discontinuity in the derivative of a wave function in the presence of an impurity. From a mathematical point of view it is natural to ask what kinds of defect can be supported by an integrable field theory without destroying integrability. Some integrable models do appear to be useful in certain special physical situations but it remains to be seen if the defects they can support are themselves relevant. The purpose of this talk is exploratory, to discover what might be possible and review a collection of ideas and questions. The main points to be addressed are: examples of integrable defects and the special role played by energy-momentum conservation and B\"acklund transformations; the description of solitons scattering with defects and some curious unanticipated effects;
the description of defects in integrable quantum field theory and associated transmission matrices; integrable field theories with boundaries revisited.

Original language	English
Title of host publication	Proceedings of the XXIX International Colloquium on Group Theoretical Mthods in Physics
Subtitle of host publication	Symmetries and Groups in Contemporary Physics
Editors	Chengming Bai, Jean-Pierre Gazeau, Mo-Lin Ge
Publisher	World Scientific Publishing
Pages	121-132
ISBN (Print)	978-981-4518-57-4
Publication status	Published - 2013

Publication series

Name	Nankai Series in Pure, Applied Mathematics and Theoretical Physics
Volume	11

Cite this

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title = "Aspects of Integrable Defects",

abstract = "Defects and impurities are ubiquitous in nature and essential for the understanding of phenomena in many domains of physics ranging from classical continuum mechanics to condensed matter physics, or cosmology. In every case, a defect is likely to be modeled by a discontinuity in a field variable, such as the abrupt change in fluid velocity across a shock, or the discontinuity in the derivative of a wave function in the presence of an impurity. From a mathematical point of view it is natural to ask what kinds of defect can be supported by an integrable field theory without destroying integrability. Some integrable models do appear to be useful in certain special physical situations but it remains to be seen if the defects they can support are themselves relevant. The purpose of this talk is exploratory, to discover what might be possible and review a collection of ideas and questions. The main points to be addressed are: examples of integrable defects and the special role played by energy-momentum conservation and B\{"}acklund transformations; the description of solitons scattering with defects and some curious unanticipated effects;the description of defects in integrable quantum field theory and associated transmission matrices; integrable field theories with boundaries revisited.",

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year = "2013",

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series = "Nankai Series in Pure, Applied Mathematics and Theoretical Physics",

publisher = "World Scientific Publishing",

pages = "121--132",

editor = "Chengming Bai and Jean-Pierre Gazeau and Mo-Lin Ge",

booktitle = "Proceedings of the XXIX International Colloquium on Group Theoretical Mthods in Physics",

address = "Singapore",

}

Aspects of Integrable Defects. / Corrigan, Ed.
Proceedings of the XXIX International Colloquium on Group Theoretical Mthods in Physics: Symmetries and Groups in Contemporary Physics. ed. / Chengming Bai; Jean-Pierre Gazeau; Mo-Lin Ge. World Scientific Publishing, 2013. p. 121-132 (Nankai Series in Pure, Applied Mathematics and Theoretical Physics; Vol. 11).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Aspects of Integrable Defects

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PY - 2013

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N2 - Defects and impurities are ubiquitous in nature and essential for the understanding of phenomena in many domains of physics ranging from classical continuum mechanics to condensed matter physics, or cosmology. In every case, a defect is likely to be modeled by a discontinuity in a field variable, such as the abrupt change in fluid velocity across a shock, or the discontinuity in the derivative of a wave function in the presence of an impurity. From a mathematical point of view it is natural to ask what kinds of defect can be supported by an integrable field theory without destroying integrability. Some integrable models do appear to be useful in certain special physical situations but it remains to be seen if the defects they can support are themselves relevant. The purpose of this talk is exploratory, to discover what might be possible and review a collection of ideas and questions. The main points to be addressed are: examples of integrable defects and the special role played by energy-momentum conservation and B\"acklund transformations; the description of solitons scattering with defects and some curious unanticipated effects;the description of defects in integrable quantum field theory and associated transmission matrices; integrable field theories with boundaries revisited.

AB - Defects and impurities are ubiquitous in nature and essential for the understanding of phenomena in many domains of physics ranging from classical continuum mechanics to condensed matter physics, or cosmology. In every case, a defect is likely to be modeled by a discontinuity in a field variable, such as the abrupt change in fluid velocity across a shock, or the discontinuity in the derivative of a wave function in the presence of an impurity. From a mathematical point of view it is natural to ask what kinds of defect can be supported by an integrable field theory without destroying integrability. Some integrable models do appear to be useful in certain special physical situations but it remains to be seen if the defects they can support are themselves relevant. The purpose of this talk is exploratory, to discover what might be possible and review a collection of ideas and questions. The main points to be addressed are: examples of integrable defects and the special role played by energy-momentum conservation and B\"acklund transformations; the description of solitons scattering with defects and some curious unanticipated effects;the description of defects in integrable quantum field theory and associated transmission matrices; integrable field theories with boundaries revisited.

M3 - Conference contribution

SN - 978-981-4518-57-4

T3 - Nankai Series in Pure, Applied Mathematics and Theoretical Physics

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BT - Proceedings of the XXIX International Colloquium on Group Theoretical Mthods in Physics

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