"Constrained system : U(1) pure gauge theory"의 두 판 사이의 차이
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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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[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:QFT]] | [[분류:QFT]] | ||
2020년 11월 13일 (금) 06:56 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
\(\mathcal{L}_{\text{free}} = \bar{\psi} (i\gamma^\mu \partial_\mu -m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\)