This book provides a detailed description of the duality between two integrable systems: the 1+1-dimensional Sine-Gordon model and the 1+1-dimensional Thirring model. While of great importance per se, this duality is only part of the target of the book. In order to reach an understanding of the subtleties involved in the duality, one has to take a journey through the properties of quantum integrable systems, building from the ground up the theory of exact S-matrices and familiarising oneself with the mathematical concept of a quantum group. The book therefore becomes an opportunity for a focussed study of integrability in its wider breadth of interest, always maintaining a clear ultimate purpose in mind: understanding the duality between bosons and fermions in 1+1 dimensions. This should make going through the book from the point of view of the reader/early-career researcher a live enterprise, as opposed to a more passive learning exercise.

Key Features:

• The book fills a gap in the existing literature, collating a vast amount scattered literature, with uniformised notation and conventions
• The book's format is ideal for use in PhD Schools and advanced graduate level mini courses, or for beginner PhD students as an introductory reference
• Originates for an invited set of lectures
• Contains a significant number of worked examples and problems, with solutions. It also presents several open-ended suggestions for literature reviews and guided learning through references

This book provides a detailed description of the duality between two integrable systems: the 1+1-dimensional Sine-Gordon model and the 1+1-dimensional Thirring model. While of great importance per se, this duality is only part of the target of the book. In order to reach an understanding of the subtleties involved in the duality, one has to take a journey through the properties of quantum integrable systems, building from the ground up the theory of exact S-matrices and familiarising oneself with the mathematical concept of a quantum group. The book therefore becomes an opportunity for a focussed study of integrability in its wider breadth of interest, always maintaining a clear ultimate purpose in mind: understanding the duality between bosons and fermions in 1+1 dimensions. This should make going through the book from the point of view of the reader/early-career researcher a live enterprise, as opposed to a more passive learning exercise.

Key Features:

• The book fills a gap in the existing literature, collating a vast amount scattered literature, with uniformised notation and conventions
• The book's format is ideal for use in PhD Schools and advanced graduate level mini courses, or for beginner PhD students as an introductory reference
• Originates for an invited set of lectures
• Contains a significant number of worked examples and problems, with solutions. It also presents several open-ended suggestions for literature reviews and guided learning through references

This book provides a detailed description of the duality between two integrable systems: the 1+1-dimensional Sine-Gordon model and the 1+1-dimensional Thirring model. While of great importance per se, this duality is only part of the target of the book. In order to reach an understanding of the subtleties involved in the duality, one has to take a journey through the properties of quantum integrable systems, building from the ground up the theory of exact S-matrices and familiarising oneself with the mathematical concept of a quantum group. The book therefore becomes an opportunity for a focussed study of integrability in its wider breadth of interest, always maintaining a clear ultimate purpose in mind: understanding the duality between bosons and fermions in 1+1 dimensions. This should make going through the book from the point of view of the reader/early-career researcher a live enterprise, as opposed to a more passive learning exercise.

Key Features:

• The book fills a gap in the existing literature, collating a vast amount scattered literature, with uniformised notation and conventions
• The book's format is ideal for use in PhD Schools and advanced graduate level mini courses, or for beginner PhD students as an introductory reference
• Originates for an invited set of lectures
• Contains a significant number of worked examples and problems, with solutions. It also presents several open-ended suggestions for literature reviews and guided learning through references