"Virasoro algebra"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
| 4번째 줄: | 4번째 줄: | ||
* A state with negative norm is called a ghost. | * A state with negative norm is called a ghost. | ||
* If a ghost is found on any level the represetation cannot occur in a unitary theory | * If a ghost is found on any level the represetation cannot occur in a unitary theory | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | <h5>Verma module</h5> | ||
| 14번째 줄: | 20번째 줄: | ||
** c<1 case = discrete representations | ** c<1 case = discrete representations | ||
** Kac determinant formula | ** Kac determinant formula | ||
| + | |||
| + | |||
| + | |||
| + | <h5>Discrete series unitary representations</h5> | ||
| + | |||
| + | * c<1 case | ||
| 24번째 줄: | 36번째 줄: | ||
<math>r = 1, 2, 3,\cdots,m-1</math> | <math>r = 1, 2, 3,\cdots,m-1</math> | ||
| + | |||
| + | <math>s= 1, 2, 3,\cdots, r</math> | ||
| − | |||
| − | |||
| 53번째 줄: | 65번째 줄: | ||
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* http://en.wikipedia.org/wiki/Virasoro_algebra | * http://en.wikipedia.org/wiki/Virasoro_algebra | ||
| + | * | ||
* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q= | * http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q= | ||
* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7= | * http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7= | ||
| − | + | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | <h5>TeX</h5> | ||
2009년 7월 28일 (화) 14:52 판
Unitarity and Ghost
- Unitarity means the inner product in the space of states is positive definite
- A state with negative norm is called a ghost.
- If a ghost is found on any level the represetation cannot occur in a unitary theory
Verma module
unitary representations
- They are classified by c>1 and c<1 case.
- c<1 case = discrete representations
- Kac determinant formula
Discrete series unitary representations
- c<1 case
\(m= 2, 3, 4.\cdots\)
\(c = 1-{6\over m(m+1)} = 0,\quad 1/2,\quad 7/10,\quad 4/5,\quad 6/7,\quad 25/28, \ldots\)
\(h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}\)
\(r = 1, 2, 3,\cdots,m-1\)
\(s= 1, 2, 3,\cdots, r\)
관련된 다른 주제들
표준적인 도서 및 추천도서
- http://search.gigapedia.com/?q=
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
참고할만한 자료
- Quantum Group Structure of the q-Deformed Virasoro Algebra
- Haihong Hu
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Virasoro_algebra
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=