"BRST quantization and cohomology"의 두 판 사이의 차이
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Faddeev-Ghost determinant==
path integral and ghost sector==
nilpotency of BRST operator==
construction of Hilbert space of states==
BRST cohomology==
applications==
books==
encyclopedia==
expositions==
articles==
blogs==
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | ==introduction | + | ==introduction== |
* [[Gauge theory|gauge theory]] = principal G-bundle<br> | * [[Gauge theory|gauge theory]] = principal G-bundle<br> | ||
| 14번째 줄: | 14번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">gauge fixing | + | <h5 style="margin: 0px; line-height: 2em;">gauge fixing== |
| 22번째 줄: | 22번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">ghost variables | + | <h5 style="margin: 0px; line-height: 2em;">ghost variables== |
* [[Faddeev–Popov ghost fields|ghost fields]]<br> | * [[Faddeev–Popov ghost fields|ghost fields]]<br> | ||
| 32번째 줄: | 32번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">Faddeev-Ghost determinant | + | <h5 style="margin: 0px; line-height: 2em;">Faddeev-Ghost determinant== |
* [http://hitoshi.berkeley.edu/230A/FPghosts.pdf Faddeev-Popov ghosts], Hitoshi Murayama<br> | * [http://hitoshi.berkeley.edu/230A/FPghosts.pdf Faddeev-Popov ghosts], Hitoshi Murayama<br> | ||
| 42번째 줄: | 42번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">path integral and ghost sector | + | <h5 style="margin: 0px; line-height: 2em;">path integral and ghost sector== |
* <math>Z = \int\!\mathcal{D}X\,\mathcal{D}c \mathcal{D}b \mathcal{D}\bar{c} \mathcal{D}\bar{b} \,e^{-\int\left(\partial X \partial \bar{X} -b_{zz}\partial_{\bar{z}}c^{z}+b_{\bar{z}\bar{z}}\partial_{z}c^{\bar{z}}\right)}</math> | * <math>Z = \int\!\mathcal{D}X\,\mathcal{D}c \mathcal{D}b \mathcal{D}\bar{c} \mathcal{D}\bar{b} \,e^{-\int\left(\partial X \partial \bar{X} -b_{zz}\partial_{\bar{z}}c^{z}+b_{\bar{z}\bar{z}}\partial_{z}c^{\bar{z}}\right)}</math> | ||
| 61번째 줄: | 61번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">nilpotency of BRST operator | + | <h5 style="margin: 0px; line-height: 2em;">nilpotency of BRST operator== |
* new, global symmetry (BRST)<br> | * new, global symmetry (BRST)<br> | ||
| 73번째 줄: | 73번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">construction of Hilbert space of states | + | <h5 style="margin: 0px; line-height: 2em;">construction of Hilbert space of states== |
* BRST charge acts on a huge space<br> | * BRST charge acts on a huge space<br> | ||
| 85번째 줄: | 85번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">BRST cohomology | + | <h5 style="margin: 0px; line-height: 2em;">BRST cohomology== |
* <math>\Lambda_{\infty}</math> semi-infinite form<br> | * <math>\Lambda_{\infty}</math> semi-infinite form<br> | ||
| 96번째 줄: | 96번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 2em;">applications | + | <h5 style="margin: 0px; line-height: 2em;">applications== |
* BRST approach to minimal models BRST approach to minimal models [http://dx.doi.org/10.1016/0550-3213%2889%2990568-3 http://dx.doi.org/10.1016/0550-3213(89)90568-3]<br> | * BRST approach to minimal models BRST approach to minimal models [http://dx.doi.org/10.1016/0550-3213%2889%2990568-3 http://dx.doi.org/10.1016/0550-3213(89)90568-3]<br> | ||
| 108번째 줄: | 108번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">related items | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">related items== |
* [[물리학과 cohomology]]<br> | * [[물리학과 cohomology]]<br> | ||
| 118번째 줄: | 118번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">books | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">books== |
* Polchinski, vol. I. $3.1-3.4, 4.2-4.3 | * Polchinski, vol. I. $3.1-3.4, 4.2-4.3 | ||
| 127번째 줄: | 127번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia== |
* http://en.wikipedia.org/wiki/BRST_quantization | * http://en.wikipedia.org/wiki/BRST_quantization | ||
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| − | <h5 style="margin: 0px; line-height: 2em;">expositions | + | <h5 style="margin: 0px; line-height: 2em;">expositions== |
* [http://www.math.sciences.univ-nantes.fr/%7Ewagemann/LAlecture.pdf Introduction to Lie algebra cohomology with a view towards BRST cohomology] ,Friedrich Wagemann, 2010-8<br> | * [http://www.math.sciences.univ-nantes.fr/%7Ewagemann/LAlecture.pdf Introduction to Lie algebra cohomology with a view towards BRST cohomology] ,Friedrich Wagemann, 2010-8<br> | ||
| 151번째 줄: | 151번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles== |
* Igor B. Frenkel, Anton M. Zeitlin, Quantum Group as Semi-infinite Cohomology | * Igor B. Frenkel, Anton M. Zeitlin, Quantum Group as Semi-infinite Cohomology | ||
| 163번째 줄: | 163번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">blogs | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">blogs== |
* [http://www.math.columbia.edu/%7Ewoit/notesonbrst.pdf http://www.math.columbia.edu/~woit/notesonbrst.pdf] | * [http://www.math.columbia.edu/%7Ewoit/notesonbrst.pdf http://www.math.columbia.edu/~woit/notesonbrst.pdf] | ||
| 184번째 줄: | 184번째 줄: | ||
| − | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">TeX | + | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">TeX == |
2012년 10월 28일 (일) 15:22 판
introduction
- gauge theory = principal G-bundle
- we require a quantization of gauge theory
- BRST quantization is one way to quantize the theory and is a part of path integral
- gauge theory allows 'local symmetry' which should be ignored to be physical
- this ignoring process leads to the cohomoloy theory.
- gauge theory allows 'local symmetry' which should be ignored to be physical
- BRST = quantization procedure of a classical system with constraints by introducing odd variables (“ghosts”)
- re-packaging of Faddeev-Popov quantization
- the conditions D = 26 and α0 = 1 for the space-time dimension D and the zero-intercept α0 of leading trajectory are required by the nilpotency QB2 = 0 of the BRS charge
gauge fixing==
ghost variables==
Faddeev-Ghost determinant==
- Faddeev-Popov ghosts, Hitoshi Murayama
path integral and ghost sector==
- \(Z = \int\!\mathcal{D}X\,\mathcal{D}c \mathcal{D}b \mathcal{D}\bar{c} \mathcal{D}\bar{b} \,e^{-\int\left(\partial X \partial \bar{X} -b_{zz}\partial_{\bar{z}}c^{z}+b_{\bar{z}\bar{z}}\partial_{z}c^{\bar{z}}\right)}\)
- \(e^{S_1(X)+S_2(b,c,\bar{b},\bar{c},\cdots,X)\)
- DX : matter and Db : ghost Dc : antighost
- bc system of \epsilon=+1 (in Faddeev–Popov ghost fields)
- \lambda=2
- c_{b,c}=-26
- [c]=-1,[b]=2
- global issues
- discrepancies in conformal gauge
- moduli spaces
- CKV
- path integral and moduli space of Riemann surfaces
- discrepancies in conformal gauge
- moduli spaces
- CKV