advanced_notions:quantum_field_theory:solitons
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advanced_notions:quantum_field_theory:solitons [2018/03/17 15:37] jakobadmin [FAQ] |
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| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
| - | [[advanced_tools:feynman_diagrams|Feynman diagrams]] do not describe everything that can happen in a [[theories:quantum_theory:quantum_field_theory|quantum field theory]]. There can be classical solutions of the field equations that describe larger lumps of field excitations that aren't describable by Feynman diagrams. | + | [[advanced_tools:feynman_diagrams|Feynman diagrams]] do not describe everything that can happen in a [[theories:quantum_field_theory:canonical|quantum field theory]]. There can be classical solutions of the field equations that describe larger lumps of field excitations that aren't describable by Feynman diagrams. |
| Classical solutions of the field equations with finite energy are called solitons. | Classical solutions of the field equations with finite energy are called solitons. | ||
| - | Such solutions are important to describe, for example, the vacuum of a theory. A famous example is the [[advanced_notions:quantum_field_theory:cd_vacuum|QCD vacuum]] which can only understand with the help of [[advanced_notions:quantum_field_theory:instantons|instantons]]. | + | Such solutions are important to describe, for example, the vacuum of a theory. A famous example is the [[advanced_notions:quantum_field_theory:qcd_vacuum|QCD vacuum]] which can only understand with the help of [[advanced_notions:quantum_field_theory:instantons|instantons]]. |
| In addition, there is an [[http://www.pbs.org/wgbh/nova/blogs/physics/2011/12/beautiful-losers-kelvins-vortex-atoms/|old dream]] that all elementary particles could be explained as topological solitons. (There are lots of problems with this idea, but at least, [[https://plus.google.com/+UrsSchreiber/posts/Z2LfHsyxgR8|instantons come somewhat close]].) | In addition, there is an [[http://www.pbs.org/wgbh/nova/blogs/physics/2011/12/beautiful-losers-kelvins-vortex-atoms/|old dream]] that all elementary particles could be explained as topological solitons. (There are lots of problems with this idea, but at least, [[https://plus.google.com/+UrsSchreiber/posts/Z2LfHsyxgR8|instantons come somewhat close]].) | ||
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| + | While solitons are rare in particle physics, they are found frequently in condensed matter physics. | ||
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| * Non-linearity of the wave equations can result in waves that get __steeper__ over time. A good example are the waves that can be observed at a beach. | * Non-linearity of the wave equations can result in waves that get __steeper__ over time. A good example are the waves that can be observed at a beach. | ||
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| + | ---- | ||
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| + | **Recommended Textbooks** | ||
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| + | * Solitons and Instantons by Ramamurti Rajaraman - is the best introductory book on solitons and related topics | ||
| + | * Topological Solitons by Manton and Sutcliff - is the second-best introductory book on solitons | ||
| + | * [[http://scipp.ucsc.edu/~haber/ph218/classicallumpsreview_Infanger.pdf|Classical lumps and their quantum descendants]] by Sidney Coleman - a "must read" lecture for anyone interested in solitons | ||
| + | * Classical Solutions in Quantum Field Theory: Solitons and Instantons by Erick Weinberg - contains several helpful chapters | ||
| + | * Classical Theory of Gauge Fields by Rubakov - is great to dive deeper and contains many alternative perspectives that can't be found anywhere else. | ||
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| + | * Quarks, Leptons & Gauge Fields by Kerson Huang - contains several extremely helpful chapters regarding solitons etc. | ||
| + | * Quantum Field Theory by Lewis H. Ryder - contains, like Huang's book - a particular nice chapter on solitons and instantons | ||
| <tabbox Researcher> | <tabbox Researcher> | ||
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| Skyrme model, the solitons, usually referred to as Skyrmions, would describe the classical limit | Skyrme model, the solitons, usually referred to as Skyrmions, would describe the classical limit | ||
| of baryons whereas mesons were associated with light quanta.<cite>https://arxiv.org/pdf/hep-th/0611180.pdf</cite></blockquote> | of baryons whereas mesons were associated with light quanta.<cite>https://arxiv.org/pdf/hep-th/0611180.pdf</cite></blockquote> | ||
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| + | ---- | ||
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| + | * Geometry of Yang-Mills Fields by M. F. ATIYAH plus chapters in | ||
| + | * Geometry of Physics by Frankel and | ||
| + | * Topology and Geometry for Physicists by Nash and Sen | ||
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| <tabbox Examples> | <tabbox Examples> | ||
advanced_notions/quantum_field_theory/solitons.1521297466.txt.gz · Last modified: 2018/03/17 14:37 (external edit)
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