"Virasoro algebra"의 두 판 사이의 차이

2009년 7월 28일 (화) 14:57 판

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

start with given c and h
\(M(c,h)\)
contains a unique maximal submodule, and its quotient is the unique (up to isomorphism) irreducible representation with highest weight

They are classified by c>1 and c<1 case.
- c<1 case = discrete representations
- Kac determinant formula

\(m= 2, 3, 4.\cdots\)

\(c = 1-{6\over m(m+1)} = 0,\quad 1/2,\quad 7/10,\quad 4/5,\quad 6/7,\quad 25/28, \ldots\)

\(h_{r,s}(c) = {((m+1)r-ms)^2-1 \over 4m(m+1)}\)

\(r = 1, 2, 3,\cdots,m-1\)

\(s= 1, 2, 3,\cdots, r\)

@@ 11번째 줄: / 11번째 줄: @@
 <h5>Verma module</h5>
+* start with given c and h
+* <math>M(c,h)</math>
+* contains a unique maximal submodule, and its quotient is the unique (up to isomorphism) irreducible representation with highest weight