advanced_tools:feynman_diagrams
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advanced_tools:feynman_diagrams [2018/02/24 16:02] jakobadmin [Student] |
advanced_tools:feynman_diagrams [2018/07/07 10:22] (current) jakobadmin [Concrete] |
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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 a 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 a few "Feynman rules," call himself or herself a field theorist, and build a credible career. Generations 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 A. Zee</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 a 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 formulas, but instead colloquial things like you would hear them during a 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 a 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. |
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| + | <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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| * 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: |
| - | * "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." A resource for signs and Feynman diagrams of the Standard Model by [[https://arxiv.org/pdf/1209.6213.pdf|Jorge C. Romao]] | + | * 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. | |
| - | <tabbox Researcher> | + | |
| - | <note tip> | + | ---- |
| - | The motto in this section is: //the higher the level of abstraction, the better//. | + | |
| - | </note> | + | |
| - | --> Common Question 1# | + | **Feynman Rules Resources:** |
| + | * "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 Abstract> |
| - | --> Common Question 2# | + | * [[https://arxiv.org/abs/math/0406251|Feynman Diagrams for Pedestrians and Mathematicians]] by M. Polyak |
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| - | <-- | ||
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| - | <tabbox Examples> | ||
| - | --> Example1# | ||
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| - | <-- | ||
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| - | --> Example2:# | ||
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| - | <-- | ||
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| <tabbox History> | <tabbox History> | ||
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| </tabbox> | </tabbox> | ||
| + | {{tag>theories:quantum_theory:quantum_field_theory}} | ||
advanced_tools/feynman_diagrams.1519484533.txt.gz · Last modified: 2018/02/24 15:02 (external edit)
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