"Constrained system : U(1) pure gauge theory"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
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==introduction== | ==introduction== | ||
| − | * U(1) pure gauge | + | * U(1) pure gauge theory : theory of light (without matter)<math>\mathcal{L}_{\text{free}} = - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}</math> |
| − | * quantization of the photon | + | * quantization of the photon field [http://www.ecm.ub.es/%7Eespriu/teaching/classes/fae/LECT4.pdf http://www.ecm.ub.es/~espriu/teaching/classes/fae/LECT4.pdf] |
** fix the gauge | ** fix the gauge | ||
** quantize unconstrained system | ** quantize unconstrained system | ||
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** we get a Hilbert space of physical states | ** we get a Hilbert space of physical states | ||
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==Gupta-Bleuler quantization of QED== | ==Gupta-Bleuler quantization of QED== | ||
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* Gupta-Bleuler Method [http://en.wikipedia.org/wiki/Gupta%E2%80%93Bleuler_formalism http://en.wikipedia.org/wiki/Gupta–Bleuler_formalism] | * Gupta-Bleuler Method [http://en.wikipedia.org/wiki/Gupta%E2%80%93Bleuler_formalism http://en.wikipedia.org/wiki/Gupta–Bleuler_formalism] | ||
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==remark== | ==remark== | ||
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* if matter exists, we get [[QED]]<math>\mathcal{L}_{\text{free}} = \bar{\psi} (i\gamma^\mu \partial_\mu -m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}</math> | * if matter exists, we get [[QED]]<math>\mathcal{L}_{\text{free}} = \bar{\psi} (i\gamma^\mu \partial_\mu -m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}</math> | ||
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==related items== | ==related items== | ||
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* [[no-ghost theorem and the construction of moonshine module and monster Lie algbera]] | * [[no-ghost theorem and the construction of moonshine module and monster Lie algbera]] | ||
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==expositions== | ==expositions== | ||
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==articles== | ==articles== | ||
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* http://www.ams.org/mathscinet | * http://www.ams.org/mathscinet | ||
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* http://dx.doi.org/ | * http://dx.doi.org/ | ||
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[[분류:physics]] | [[분류:physics]] | ||
2020년 12월 28일 (월) 04:15 판
introduction
- U(1) pure gauge theory : theory of light (without matter)\(\mathcal{L}_{\text{free}} = - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\)
- quantization of the photon field http://www.ecm.ub.es/~espriu/teaching/classes/fae/LECT4.pdf
- fix the gauge
- quantize unconstrained system
- gives physical and unphysical states (negative norm states)
- impose the constraint condition to remove negative norm states
- we get a Hilbert space of physical states
Gupta-Bleuler quantization of QED
- Gupta-Bleuler Method http://en.wikipedia.org/wiki/Gupta–Bleuler_formalism
remark
- if matter exists, we get QED\(\mathcal{L}_{\text{free}} = \bar{\psi} (i\gamma^\mu \partial_\mu -m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\)