models:standard_model:qed
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models:standard_model:qed [2018/03/15 10:37] jakobadmin [Researcher] |
models:standard_model:qed [2018/05/12 09:20] jakobadmin [Intuitive] |
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| + | <WRAP lag>$ \ L = \bar {\Psi}(i \gamma^{\mu }\partial_{\mu} + q\gamma^{\mu}A_{\mu} - m)\Psi + \frac{1}{16 \pi}F_{\alpha \beta}F^{\alpha \beta} $</WRAP> | ||
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| ====== Quantum Electrodynamics ====== | ====== Quantum Electrodynamics ====== | ||
| - | <tabbox Why is it interesting?> | + | //see also [[models:standard_model]] and [[models:classical_electrodynamics]]// |
| - | Quantum electrodynamics (QED) is the best theory of electric interactions that we have. | ||
| - | It accurately describes how elementary particles like electrons interact with each other and with light. | + | <tabbox Intuitive> |
| + | Quantum electrodynamics is the correct model of electromagnetic interactions. It is a model in the framework of [[theories:quantum_field_theory|quantum field theory]]. | ||
| + | ---- | ||
| - | <tabbox Layman> | + | * The best non-technical introduction to quantum electrodynamics is Quantum Electrodynamics by Richard P. Feynman |
| - | + | ||
| - | * The best layman introduction to quantum electrodynamics is Quantum Electrodynamics by Richard P. Feynman | + | |
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| - | <tabbox Student> | + | <tabbox Concrete> |
| - | Quantum electrodynamics is a [[theories:quantum_theory:quantum_field_theory|quantum field theory]] of electrodynamics. At its heart is a [[advanced_tools:gauge_symmetry|gauge symmetry]] called local $U(1)$ symmetry. | + | Quantum electrodynamics is a [[theories:quantum_field_theory:canonical|quantum field theory]] of electrodynamics. At its heart is a [[advanced_tools:gauge_symmetry|gauge symmetry]] called local $U(1)$ symmetry. |
| In practice, we use quantum electrodynamics to describe electrodynamical interactions between charged particles through elementary particles called photons. | In practice, we use quantum electrodynamics to describe electrodynamical interactions between charged particles through elementary particles called photons. | ||
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| Photons are the fundamental excitations of the electrodynamic field. | Photons are the fundamental excitations of the electrodynamic field. | ||
| - | There are two frameworks to calculate things in quantum electrodynamics: either using [[advanced_tools:feynman_diagrams|Feynman diagrams]] (= the [[frameworks:hamiltonian_formalism|Hamiltonian framework]]) or using [[advanced_tools:path_integral|path integrals]] (= the [[frameworks:lagrangian_formalism|Lagrangian framework]]). | + | There are two frameworks to calculate things in quantum electrodynamics: either using [[advanced_tools:feynman_diagrams|Feynman diagrams]] (= the [[formalisms:hamiltonian_formalism|Hamiltonian framework]]) or using [[theories:quantum_mechanics:path_integral|path integrals]] (= the [[formalisms:lagrangian_formalism|Lagrangian framework]]). |
| ---- | ---- | ||
| - | The QED Lagrangian reads | ||
| - | |||
| - | $$L = \bar {\Psi}(i \gamma^{\mu }\partial_{\mu} + q\gamma^{\mu}A_{\mu} - m)\Psi + \frac{1}{16 \pi}F_{\alpha \beta}F^{\alpha \beta} . $$ | ||
| See also https://en.wikipedia.org/wiki/Quantum_electrodynamics#Mathematics | See also https://en.wikipedia.org/wiki/Quantum_electrodynamics#Mathematics | ||
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| - | <tabbox Researcher> | + | <tabbox Abstract> |
| **Additional Conserved Charge** | **Additional Conserved Charge** | ||
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| - | This charge generates an __additional global symmetry__ and it | + | This charge generates an __additional global symmetry__. |
| - | <blockquote>measures the magnetic flux of a line operator $H(C)$ (the "`t Hooft line operator") which is supported on a line $C$ which links the $S^2$. It corresponds to the worldline of a probe magnetic monopole, and $Q$ measures the magnetic flux of the monopole in the same way that $\int_{S^2} \star F$ measures the electric flux on the worldline of an electric charge. These are called 1-form global symmetries, because the charged operators are supported on lines. | + | <blockquote>The conserved charge is the magnetic flux associated to the U(1) gauge |
| + | symmetry.<cite>[[http://www.damtp.cam.ac.uk/user/tong/qhe/qhe.pdf|David Tong page 169]]</cite></blockquote> | ||
| + | |||
| + | Formulated differently: | ||
| + | <blockquote>[It] measures the magnetic flux of a line operator $H(C)$ (the "`t Hooft line operator") which is supported on a line $C$ which links the $S^2$. It corresponds to the worldline of a probe magnetic monopole, and $Q$ measures the magnetic flux of the monopole in the same way that $\int_{S^2} \star F$ measures the electric flux on the worldline of an electric charge. These are called 1-form global symmetries, because the charged operators are supported on lines. | ||
| The same story goes through in any dimension $d>2$. We obtain a $(d-3)$-form global symmetry, meaning the charged operators are supported on $(d-3)$-manifolds which link a 2-sphere over which we measure the charge $\int_{S^2} F$. | The same story goes through in any dimension $d>2$. We obtain a $(d-3)$-form global symmetry, meaning the charged operators are supported on $(d-3)$-manifolds which link a 2-sphere over which we measure the charge $\int_{S^2} F$. | ||
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| - | <tabbox FAQ> | + | <tabbox Why is it interesting?> |
| + | |||
| + | Quantum electrodynamics (QED) is the best theory of electromagnetic interactions that we have. | ||
| + | |||
| + | It's a crucial part of the [[models:standard_model|standard model]] and accurately describes how elementary particles like electrons interact with each other and with light. | ||
| + | |||
| + | In addition, it's one of the best-tested theories in the history of science and so far, passed all precision tests. | ||
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| <tabbox History> | <tabbox History> | ||
| + | * "QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga" by Schweber | ||
| * The notion “quantum electrodynamics” was invented by Paul Dirac in [[http://wwwhome.lorentz.leidenuniv.nl/~boyarsky/media/Proc.R.Soc.Lond.-1927-Dirac-243-65.pdf|The quantum theory of emission and absorption of radiation]] | * The notion “quantum electrodynamics” was invented by Paul Dirac in [[http://wwwhome.lorentz.leidenuniv.nl/~boyarsky/media/Proc.R.Soc.Lond.-1927-Dirac-243-65.pdf|The quantum theory of emission and absorption of radiation]] | ||
| </tabbox> | </tabbox> | ||
models/standard_model/qed.txt · Last modified: 2018/05/12 09:21 by jakobadmin
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