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advanced_notions:quantum_field_theory:solitons [2018/03/26 11:14]
jakobadmin [Researcher]
advanced_notions:quantum_field_theory:solitons [2018/05/05 12:38] (current)
jakobadmin ↷ Links adapted because of a move operation
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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. ​
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 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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 +**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> ​
advanced_notions/quantum_field_theory/solitons.1522055643.txt.gz · Last modified: 2018/03/26 09:14 (external edit)