advanced_tools:feynman_diagrams
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advanced_tools:feynman_diagrams [2018/04/14 09:19] aresmarrero [Intuitive] |
advanced_tools:feynman_diagrams [2018/07/07 10:22] (current) jakobadmin [Concrete] |
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| - | {{ :advanced_notions:quantum_field_theory:virtualparticles.png?nolink&350|}} | ||
| + | {{ :advanced_tools:320px-feynmandiagram.png?nolink&300|}} | ||
| - | Feynman diagrams are a pictorial way to keep track of terms in [[theories:quantum_field_theory|quantum field theory]] calculations. Each element of a Feynman diagram represents a different term in our calculation. | ||
| - | An example can be seen on the right-hand side. | + | |
| + | 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. | ||
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| + | 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. | ||
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| + | {{ :advanced_notions:quantum_field_theory:virtualparticles.png?nolink&250|}} | ||
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| + | 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. | ||
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| + | 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. | ||
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| + | 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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| * 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 | ||
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| + | Take note that the usage of Feynman diagrams is not limited to Quantum Mechanics. See: | ||
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| + | * 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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| <tabbox Abstract> | <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> | + | |
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advanced_tools/feynman_diagrams.1523690394.txt.gz · Last modified: 2018/04/14 07:19 (external edit)
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