S*********g
发帖数: 5298 | 1 It's a concept of Virasoro Algebra and conformal field theory.
The OPE (Operator Product Expansion) of Energy-momentum tensor is
T(z)T(0) \sim c/2/z^4 + 2T(0)/z^2+\partial T(0)/z z is complex
Here c is the central charge.
It's determined by the short-distance behavior of the theory.
free boson: c=1
free fermion: c=1/2
ghost: c=-26 | S*********g
发帖数: 5298 | 2 The classical generators of local conformal transformation obey the
algebra with c=0 while quantum ones obey an identical algebra except
nozero central charge.
Agian, let's expand Energy-momentum tensor:
T(z) = \sum_{n \in Z} z^{-n-2} L_n
\bar{T}(z) = \sum_{n \in Z} z^{-n-2} \bar{L}_n
L_n and \bar{L}_n are generators of local conformal transformation
on the Hilbert space.
The algebra is
[L_n,L_m]=(n-m)L_{n+m}+c/12 n(n^2-1)\delta_{n+m,0}
[L_n,\bar{L}_m]=0
[\bar{L}_n,\bar{L}_m]=(n-m)\bar{L}_{n+m}+
【在 S*********g 的大作中提到】
: It's a concept of Virasoro Algebra and conformal field theory.
: The OPE (Operator Product Expansion) of Energy-momentum tensor is
: T(z)T(0) \sim c/2/z^4 + 2T(0)/z^2+\partial T(0)/z z is complex
: Here c is the central charge.
: It's determined by the short-distance behavior of the theory.
: free boson: c=1
: free fermion: c=1/2
: ghost: c=-26
| S*********g
发帖数: 5298 | 3 See:
Conformal Field Theory
by
Philippe Di Francesco et al
I learned this stuff from
String theory Vol. I
by Joseph Polchinski |
|
