"Gauge theory"의 두 판 사이의 차이

2010년 1월 26일 (화) 14:03 판

a gauge field is defined as a four-vector field with the freedom of gauge transformation, and it corresponds to massless particlas of spin one

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

Now we have a Lagrangian with interaction terms.

local phase transformation of fields
\(\psi(x) \to e^{i\alpha(x)}\psi(x)\)
gauge transformation of electromagnetic field
\(A_{\mu}(x) \to A_{\mu}(x)+\frac{1}{e}\partial_{\mu}\alpha(x)}\)
Look at the QED page

3d Chern-Simons theory on \(\Sigma\times \mathbb R^{1}\) with gauge choice \(A_0=0\) is the moduli space of flat connections on \(\Sigma\).
analogy with class field theory
replace \(\Sigma\) by \(spec O_K\)
then flat connection on \(spec O_K\) is given by Homomorphism group the absolute Galois group Gal(\barQ/K)->U(1)
Now from An's article,

2010년 1월 11일 (월) 09:05 판 (원본 보기) http://bomber0.myid.net/ (토론) ← 이전 편집		2010년 1월 26일 (화) 14:03 판 (원본 보기) http://bomber0.myid.net/ (토론) 다음 편집 →
95번째 줄:		95번째 줄:

	* http://www.google.com/search?hl=en&rls=IBMA,IBMA:2008-50,IBMA:en&q=brief+introduction+to+principal+bundles+connections&aq=f&oq=&aqi=<br>		* http://www.google.com/search?hl=en&rls=IBMA,IBMA:2008-50,IBMA:en&q=brief+introduction+to+principal+bundles+connections&aq=f&oq=&aqi=<br>
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