"Constrained system : U(1) pure gauge theory"의 두 판 사이의 차이

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11번째 줄: 11번째 줄:
 
[http://www.ecm.ub.es/%7Eespriu/teaching/classes/fae/LECT4.pdf http://www.ecm.ub.es/~espriu/teaching/classes/fae/LECT4.pdf]
 
[http://www.ecm.ub.es/%7Eespriu/teaching/classes/fae/LECT4.pdf http://www.ecm.ub.es/~espriu/teaching/classes/fae/LECT4.pdf]
  
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gives physical and unphysical states
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fix the gauge
  
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Hilbert space of physical states
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quantize unconstrained system
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gives physical and unphysical states (negative norm states)
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 +
impose the constraint condition to remove negative norm states
 +
 
 +
we get a Hilbert space of physical states
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Gupta-Bleuler Method http://en.wikipedia.org/wiki/Gupta%E2%80%93Bleuler_formalism
  
 
 
 
 
  
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quantize unconstrained system and then impose the constraint
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28번째 줄: 36번째 줄:
  
 
<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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<h5>introduction</h5>
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<h5>history</h5>
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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<h5>related items</h5>
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5>
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* http://en.wikipedia.org/wiki/
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* http://www.scholarpedia.org/
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* [http://eom.springer.de/ http://eom.springer.de]
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* http://www.proofwiki.org/wiki/
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* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
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<h5>books</h5>
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* [[2011년 books and articles]]
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* http://library.nu/search?q=
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* http://library.nu/search?q=
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<h5>expositions</h5>
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5>
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* http://www.ams.org/mathscinet
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* http://www.zentralblatt-math.org/zmath/en/
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* http://arxiv.org/
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* http://www.pdf-search.org/
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* http://pythagoras0.springnote.com/
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
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* http://dx.doi.org/
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<h5>question and answers(Math Overflow)</h5>
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* http://mathoverflow.net/search?q=
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* http://math.stackexchange.com/search?q=
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* http://physics.stackexchange.com/search?q=
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<h5>blogs</h5>
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*  구글 블로그 검색<br>
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**  http://blogsearch.google.com/blogsearch?q=<br>
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** http://blogsearch.google.com/blogsearch?q=
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* http://ncatlab.org/nlab/show/HomePage
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<h5>experts on the field</h5>
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* http://arxiv.org/
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<h5>links</h5>
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
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* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]

2011년 9월 24일 (토) 06:14 판

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%E2%80%93Bleuler_formalism

 

 

 

 

remark

if matter exists, we get QED

\(\mathcal{L}_{\text{free}} = \bar{\psi} (i\gamma^\mu \partial_\mu -m)\psi - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}\)

 

 

introduction

 

 

history

 

 

related items

 

 

encyclopedia

 

 

books

 

 

 

expositions

 

 

articles

 

 

 

question and answers(Math Overflow)

 

 

 

blogs

 

 

experts on the field

 

 

links
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