"Virasoro algebra"의 두 판 사이의 차이
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| 16번째 줄: | 16번째 줄: | ||
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| + | <math>m= 2, 3, 4.\cdots</math> | ||
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| + | <math>c = 1-{6\over m(m+1)} = 0,\quad 1/2,\quad 7/10,\quad 4/5,\quad 6/7,\quad 25/28, \ldots</math> | ||
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| + | <math>h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}</math> | ||
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| + | <math>r = 1, 2, 3,\cdots,m-1</math> | ||
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| + | The irreducible lowest weight representation with eigenvalues ''h'' and ''c'' is unitary if and only if either ''c''≥1 and ''h''≥0, or ''c'' is one of the values for '', .... and ''h'' is one of the values :<math> h</math> for '' and ''s''= 1, 2, 3, ..., ''r''. | ||
| 40번째 줄: | 52번째 줄: | ||
** Haihong Hu | ** Haihong Hu | ||
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
| − | * http://en.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://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= | ||
* 다음백과사전 http://enc.daum.net/dic100/search.do?q=<br> | * 다음백과사전 http://enc.daum.net/dic100/search.do?q=<br> | ||
2009년 7월 27일 (월) 19:21 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
unitary representations
- They are classified by c>1 and c<1 case.
- c<1 case = discrete representations
- Kac determinant formula
\(m= 2, 3, 4.\cdots\)
\(c = 1-{6\over m(m+1)} = 0,\quad 1/2,\quad 7/10,\quad 4/5,\quad 6/7,\quad 25/28, \ldots\)
\(h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}\)
\(r = 1, 2, 3,\cdots,m-1\)
The irreducible lowest weight representation with eigenvalues h and c is unitary if and only if either c≥1 and h≥0, or c is one of the values for , .... and h is one of the values \[ h\] for and s= 1, 2, 3, ..., r.
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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=
- 다음백과사전 http://enc.daum.net/dic100/search.do?q=