"Constrained system : U(1) pure gauge theory"의 두 판 사이의 차이
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| − | + | <h5>introduction</h5> | |
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| − | impose the constraint condition to remove negative norm states | + | * U(1) pure gauge theory : theory of light (without matter)<br><math>\mathcal{L}_{\text{free}} = - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}</math><br> |
| − | + | * 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]<br> | |
| − | we get a Hilbert space of physical states | + | ** fix the gauge |
| − | + | ** quantize unconstrained system | |
| − | Gupta-Bleuler Method http://en.wikipedia.org/wiki/Gupta%E2%80%93Bleuler_formalism | + | ** 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 Method [http://en.wikipedia.org/wiki/Gupta%E2%80%93Bleuler_formalism http://en.wikipedia.org/wiki/Gupta–Bleuler_formalism] | ||
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<math>\mathcal{L}_{\text{free}} = \bar{\psi} (i\gamma^\mu \partial_\mu -m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}</math> | <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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| 56번째 줄: | 37번째 줄: | ||
<h5>related items</h5> | <h5>related items</h5> | ||
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| + | * [[no-ghost theorem and the construction of moonshine module and monster Lie algbera]] | ||
2011년 9월 24일 (토) 07:22 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 Method http://en.wikipedia.org/wiki/Gupta–Bleuler_formalism
remark
if matter exists, we get QED
\(\mathcal{L}_{\text{free}} = \bar{\psi} (i\gamma^\mu \partial_\mu -m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\)
history
encyclopedia
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- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
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- http://arxiv.org/
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- http://dx.doi.org/
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