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 ====== Feynman Diagrams ====== ====== Feynman Diagrams ======
  
-<​tabbox ​Why is it interesting?​+<​tabbox ​Intuitive
  
-<​blockquote>​+{{ :​advanced_tools:​320px-feynmandiagram.png?​nolink&​300|}}
  
-Feynman’s diagrams and rules were a sort of bookkeeping-by-picture process that miraculously captured all the details of the standard model in a series of diagrams; they allowed people less talented than Feynman to perform the most complex calculations carefully and correctly. Many of the great advances in physics are like this; they codify and make routine what was formerly almost impossible to think about.Whenever I have a new problem to work on—in physics or options theory—the first major struggle is to gain some intuition about how to proceed; the second struggle is to transform this intuition into something more formulaic, a set of rules anyone can follow, rules that no longer require the original insight itself. In this way, one person’s breakthrough becomes everybody’s possession. 
  
-<​cite>​From My Life As A Quant by Emanuel Derman</​cite>​ 
-</​blockquote>​ 
  
-<​blockquote>​ +Feynman ​diagrams are a pictorial way to keep track of terms in [[theories:​quantum_field_theory:​canonical|quantum field theory]] calculations. Each element of a Feynman ​diagram represents ​different term in our calculation.
-Julian Schwinger once said rather bitterly that "Feynman ​brought ​quantum field theory ​to the masses,"​ by which he meant that any dullard could memorize ​few "Feynman ​rules,"​ call himself or herself ​field theorist, and build a credible careerGenerations learned Feynman diagrams without understanding field theory. Heavens to Betsy, there are still university professors like that walking around!+
  
-<​cite>​from the preface of Feynman's [[http://​press.princeton.edu/​chapters/​i8169.html|The Strange Theory of Light and Matter]] by AZee</​cite>​ +The thing is that we can't calculate things in quantum field theory exactly, but only using a perturbation approach (Taylor series). The first term in this approximation to the correct result yields the biggest contribution ​and thus is the most important part
-</​blockquote>​+
  
-<tabbox Layman> ​+{{ :​advanced_notions:​quantum_field_theory:​virtualparticles.png?​nolink&​250|}}
  
-<note tip> +An example can be seen on the right-hand side. In this example two electrons scatter. They do this by exchanging a photon $\gamma$which is denoted by wiggly line. After the exchange of the photon the two electrons move away from each other with different momenta.  
-Explanations in this section should contain no formulasbut instead colloquial things like you would hear them during ​coffee break or at a cocktail party+ 
-</​note>​ +In the first order approximation (i.e. when we only consider the first term in the approximation series mentioned above) the two electrons scatter by only exchanging a photon. 
-   + 
-<​tabbox ​Student+However, ​at the next order we also take into account that the photon can become ​virtual electron-positron pair during this exchange. This will not happen with a high probability but is possible. Even more unlikely, but also possible, is that the virtual electron interacts with one of our in-going electrons via another photon. The total probability amplitude for the scattering to happen is the sum over all such possibilities
 + 
 + 
 +<​tabbox ​Concrete
  
   * [[https://​arxiv.org/​pdf/​1602.04182.pdf|Feynman Diagrams for Beginners]] by Krešimir Kumericki   * [[https://​arxiv.org/​pdf/​1602.04182.pdf|Feynman Diagrams for Beginners]] by Krešimir Kumericki
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   * R.D. Mattuck: A Guide to Feynman Diagrams in the Many-body Problem   * R.D. Mattuck: A Guide to Feynman Diagrams in the Many-body Problem
   * For the derivation of the Feynman rules for a given theory see section 2 of [[http://​cds.cern.ch/​record/​186259/​|Diagrammar]] by Veltman and '​tHooft   * For the derivation of the Feynman rules for a given theory see section 2 of [[http://​cds.cern.ch/​record/​186259/​|Diagrammar]] by Veltman and '​tHooft
 +
 +Take note that the usage of Feynman diagrams is not limited to Quantum Mechanics. See:
 +
 +  * A. Thorndike, “Using Feynman diagrams to solve the classical harmonic oscillator,​” Am. J. Phys. 68 (2), 155-159 (2000)
 +  * R. Penco and D. Mauro, “Perturbation theory via Feynman diagrams in classical mechanics,​” hep-th/​0605061. ​
  
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   * "When performing a full calculation within the Standard Model or its extensions, it is crucial that one utilizes a consistent set of signs for the gauge couplings and gauge fields. Unfortunately,​ the literature is plagued with differing signs and notations. We present all Standard Model Feynman rules, including ghosts, in a convention-independent notation, and we table the conventions in close to 40 books and reviews."​ from [[https://​arxiv.org/​pdf/​1209.6213.pdf|A resource for signs and Feynman diagrams of the Standard Model]] by Jorge C. Romao   * "When performing a full calculation within the Standard Model or its extensions, it is crucial that one utilizes a consistent set of signs for the gauge couplings and gauge fields. Unfortunately,​ the literature is plagued with differing signs and notations. We present all Standard Model Feynman rules, including ghosts, in a convention-independent notation, and we table the conventions in close to 40 books and reviews."​ from [[https://​arxiv.org/​pdf/​1209.6213.pdf|A resource for signs and Feynman diagrams of the Standard Model]] by Jorge C. Romao
    
-<​tabbox ​Researcher+<​tabbox ​Abstract
  
-<note tip> +  * [[https://arxiv.org/abs/math/0406251|Feynman Diagrams for Pedestrians and Mathematicians]] by M. Polyak
-The motto in this section is: //the higher the level of abstraction,​ the better//+
-</note>+
  
---> Common Question 1# 
  
-  
-<-- 
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---> Common Question 2# 
- 
-  
-<-- 
-  ​ 
-<tabbox Examples> ​ 
- 
---> Example1# 
- 
-  
-<-- 
- 
---> Example2:# 
- 
-  
-<-- 
   ​   ​
 <tabbox History> ​ <tabbox History> ​
advanced_tools/feynman_diagrams.1520864953.txt.gz · Last modified: 2018/03/12 14:29 (external edit)